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Problem_Set_02_Solutions

Course: BIO SCI mcb 121, Spring 2012
School: UC Davis
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121 MCB Spring 2011 Problem Set 2: 1. You have taken a job in a biotech company that studies different metabolic enzymes for commercial use. Your first assignment is to study the enzymatic properties of galactokinase from S. cerevisiae, the product of the GAL1 gene. You decide on a strategy to express Gal1 protein in E. coli and purify the protein for your enzymatic studies. At your disposal is a PCR machine, a...

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121 MCB Spring 2011 Problem Set 2: 1. You have taken a job in a biotech company that studies different metabolic enzymes for commercial use. Your first assignment is to study the enzymatic properties of galactokinase from S. cerevisiae, the product of the GAL1 gene. You decide on a strategy to express Gal1 protein in E. coli and purify the protein for your enzymatic studies. At your disposal is a PCR machine, a DNA oligo synthesizer, yeast genomic DNA, and an expression vector for E. coli (shown below). This expression system uses a promoter from the bacteriophage T7. Shown at the bottom is a portion of the multiple cloning site (MCS) in which you will insert your DNA. Design oligonucleotide primers that will allow you to insert the GAL1 gene into this expression vector, using the SacI (GAGCTC) and XbaI (TCTAGA) restriction sites. The total length of each primer should be 20 nucleotides. 1 Answer: What you need to know: Sequence of SacI and XbaI restriction sites (given information) SacI XbaI 5'-GAGCTC-3' 5'-TCTAGA-3' Sequence of the 14 most 5' bases of GAL1 (given in class Lecture 2 or via the SGD web site) 5'-ATG-ACT-AAA-TCT-CA-3' (start codon underlined) Sequence of the complement of the 14 most 3' bases of GAL1 (including a stop codon) (derived from sequence) Sense strand: 5'-TA-TAT-GAA-TTA-TAA-3'(stop codon underlined) Complement: 3'-AT-ATA-CTT-AAT-ATT-5' So: 5' Forward Primer (total length = 20 bases) This simply consists of the 5' sequences of GAL1 preceded by the SacI site: 5'- GAGCTCATGACTAAATCTCA-3' (SacI site underlined) 3' Reverse Primer (total length = 20 bases) This consists of the complementary 3' sequences preceded by the XbaI site: 5'-TCTAGATTATAATTCATATA-3' (XbaI site underlined; note this sequence is written in the 5' 3' direction) 2 2. You are the president of a biotech company that isolates and sells novel restriction endonucleases. One of your employees has isolated two isoschizomers of Sau3A I (recognizes GATC), one called EcoB II and EcoB IV. EcoB II generates a two base 5' overhang and EcoB IV generates a four base 3' overhang following cleavage. You are putting together the new company catalog and you are checking to make sure that all of the information is correct for describing these new enzymes. What is an isoschizomer? From what organism were these enzymes isolated? What are the reaction products produced following cleavage with each of these enzymes? In your company catalog, can you state that your new enzymes are compatible for cloning DNA fragments into BamH I sites? Why or why not? What organism: Eco = E. coli strain B Reaction products: Eco B II: two base 5' overhang: 5' 3' NNNNGATCNNNN3' NNNNCTAGNNNN5' 5' 3' NNNNG3' NNNNCTA5' 5' ATCNNNN3' 3' GNNNN5' EcoB IV: four base 3' overhang: NNNNGATCNNNN3' 3' NNNNCTAGNNNN5' Compatability with BamHI: Neither enzyme is compatible with BamHI. While the GATC recognition sequence of both is imbedded within the BamHI sequence (GGATCC), digestion with BamHI yields a 4 base 5' overhang that cannot anneal with the reaction products of either EcoB II or EcoB IV. 5' 5' NNNNGATC3' 3' NNNN5' NNNN3' 3' CTAGNNNN5' 5' 3 3. To prepare a genomic DNA it library, is necessary to fragment the genome so that it can be cloned into a vector. A common method is to use a restriction endonuclease. How many different genomic fragments would you expect if you digested human genomic DNA 9 with Sau3A I? (Note: the haploid human genome is ~3.2 x 10 base pairs.) How many total fragments would you get if you used EcoR I? A restriction nuclease that recognizes a four-base-pair site will cut on average 1 out of 256 fourbase-pair sites (1/4)4 . Thus, you would expect on the order of 1.3 x 107 different fragments (3.2 x 109/256) from a Sau3A digestion of human DNA. Similarly, you would expect on the order of 7.8 x 105 different fragments (3.2 x 109 /4096) from an EcoRI digestion. However, because the genome is diploid, there would be 15.6 x 105 total fragments produced per genome (2 x 7.8 x 105). These estimates are based on the assumptions that the genome is 50% GC and that the sequence is random: neither of which is true, but they won't lead you far astray. Genomic libraries are often made from fragments obtained by cleaving the DNA with Sau3A I such that only partial digestion of the DNA is achieved. Why? A set of overlapping DNA fragments will be generated by partial digestion. In class we discussed on important reason to do this, which is to help ensure that an entire yeast gene would be contained within one piece of DNA. With the genomes of higher eukaryotes this isn't possible using genomic DNA. Here, libraries constructed from sets of overlapping fragments of a genome are still valuable because they can be used to arrange cloned sequences in their original order on the chromosomes, and thus obtain the DNA sequence of a long stretch of DNA. Overlapping clones were crucial in the sequencing of the human genome. 4. In the very first round of PCR using genomic DNA, the DNA primers prime synthesis that terminates only when the cycle ends (or if a random end of DNA is encountered). Yet by the end of 20 to 30 cycles, the only visible product is defined precisely by the ends of the DNA primers. In what cycle is a double stranded fragment of the correct size first generated? It is at the end of the third cycle when the first product appears where the ends correspond fully to the DNA primers used. See the diagram in Lecture 3 for how this works. 5. The two strands of 4 phage DNA differ from each other in their GC content. Owing to this property, they can be separated in an alkaline cesium chloride gradient (the alkalinity denatures the duplex DNA). When the RNA synthesized by 4 phage is isolated from infected E. coli cells, it is found to form RNA-DNA hybrids with both strands of 4 DNA. What does this result tell you? Answer: Because RNA can hybridize to both strands, the RNA must be transcribed from both strands. This does not mean, however, that both strands are used as a template for each gene. The expectation is that different genes are transcribed in different directions along the DNA. The most direct test would be to purify a specific RNA coding for a specific protein and then hybridize it to the T4 genome. Only one strand of the genomic DNA should hybridize to the purified RNA. 4
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UC Davis - BIO SCI - mcb 121
MCB 121 Spring 2011 Problem Set 3 Problems 1-4 You are studying galactose metabolism in a new species of yeast. You have purified a novel protein important for galactose metabolism and have called it Gal400p. You have raised antibodies (Ab) against this p
UC Davis - BIO SCI - mcb 121
MCB 121 Spring 2011 Problem Set 3 Problems 1-4 You are studying galactose metabolism in a new species of yeast. You have purified a novel protein important for galactose metabolism and have called it Gal400p. You have raised antibodies (Ab) against this p
UC Davis - BIO SCI - mcb 121
MCB 121 Spring 2011: Study Problem Set 4 Here is the genetic code to use for this problem set:11. Before the triplet nature of the genetic code was established, it was proposed that message RNA might be read in overlapping triplets. For example, the seq
UC Davis - BIO SCI - mcb 121
MCB 121 Spring 2011: Study Problem Set 4 Here is the genetic code to use for this problem set:11. Before the triplet nature of the genetic code was established, it was proposed that message RNA might be read in overlapping triplets. For example, the seq
UC Davis - BIO SCI - mcb 121
MCB 121 2011 Dr. Ted Powers Supplement to Problem Set 4Puromycin and the Classical Model for Translational elongation1Classical Model for Translational ElongationKey features:transfer of P site amino acid to A site translocation of tRNAs on both subu
UC Davis - BIO SCI - mcb 121
MCB 121 Spring 2011: Problem Set 5 1. Over the years, a comprehensive set of temperature sensitive mutants involved in DNA replication in E. coli has been isolated and studied, defining the dna genes. These mutants can be divided into two classes, based o
UC Davis - BIO SCI - mcb 121
MCB 121 Spring 2011: Problem Set 5 Solutions 1. Over the years, a comprehensive set of temperature sensitive mutants involved in DNA replication in E. coli has been isolated and studied, defining the dna genes. These mutants can be divided into two classe
UC Davis - BIO SCI - mcb 121
MCB 121 Spring 2011: Problem Set 6 Solutions 1a. Consider the topology of a 10 kb (10,000 base pairs) circular plasmid, named pBR600, that resides inside of a bacterial cell. This plasmid normally displays 5 negative superhelical turns (i.e., supercoiling
UC Davis - BIO SCI - mcb 121
MCB 121 Spring 2011: Problem Set 7 Solutions 1. What evidence can you point to that suggests a common origin for the evolution of transcription between prokaryotes and eukaryotes? Answer: Some of the subunits in RNA polymerase II from eukaryotes are homol
UC Davis - BIO SCI - mcb 121
MCB 121 Spring 2011: Problem Set 8 Solutions 1. Which of the following describes a complete nucleosome as it exists in a mammalian cell nucleus? a. 2(H2A), 2(H2B), 1(H3), 1(H4), ~146 base pairs of DNA b. 2(H2A), 2(H2B), 2(H3), 2(H4), ~200 base pairs of DN
UC Davis - BIO SCI - mcb 121
MCB 121 2011 Sample Quiz I Questions Refer to the Genetic Code when necessary:1I) (Questions 1-4) Consider the following (simplified) pathways for head and tail formation for bacteriophage T4:One new temperature sensitive mutant (Gene X) of T4 has been
UC Davis - BIO SCI - mcb 121
George Mason - MATH - 214
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UC Davis - BIO SCI - mcb 121
MCB 121 2011 Sample Quiz II QuestionsWobble Pairing: 5' Base of tRNA anticodon U G I 3' Base of codon G U C, U, A11) Below is a schematic drawing of a human mRNA, showing potential for base-pairing interactions in the 5' UTR between three sequence elem
George Mason - MATH - 214
a./l 2 tv.Se?a+a.ttoa o/ vna *lt-c .'k= acfw_+8 ,#:a0*);o,(.1 uot'tta*t/0 - sat'Xil,t s eLofian7bcF(dxlar=5k+J-t xG) =Xo#- s(x*i)f&=frae =>.-/ \XIAi=-zrrtx&) =1L)+C=Ko-+("*3)"tb t#= r-xlxb)=Ex,2-Sofu"lhis IVP|t#-3Y+tlrh)
UC Davis - BIO SCI - mcb 121
George Mason - MATH - 214
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UC Davis - BIO SCI - mcb 121
MCB 121 Spring 2011: Sample Quiz 3 I) (Problems 1-4) 1) Tetrahymena telomerase RNA (TER) provides a template that produces the following sequence for the G-rich strand of the telomere: 5'-TTGGGG-3'. The template portion of TER that encodes this sequence i
George Mason - MATH - 214
l,lrn2/tl.t-, /, J^@.aratna-A,rra9?*P@/ft/r)F,'d ratqra-ri'y !"^*(tl = e- J Ptt)o(tft'* 2?=tlFex ,l/u H),=e#Pzrtr",uAtt(+D(2I,e*-e(bdeg'n *gLz3=/ao6.? ctar"4ddH:al"tLp/t) = eJoH = z &, t (,:rf FH r'r ft.rr,4 q r%.,u
UC Davis - BIO SCI - mcb 121
George Mason - MATH - 214
f/f ofit,+,Leafu-oEx.I (at= xJ(/ - l+2A(cfw_,Lt(n =oGlt,*(*+Llrt-= t.lt)=o=Iir _ (cfw__/) =o,U,Ji fr.i,;o,l:h*?bard,ta-h'L(orr-t /+I:o('*At f c =o^lx,lHr, h c/'u<e do=cfw_t,)9 F,'na/=2N'-l2&a^"1 gah's fu,n-/*,fThTl2,-lx-,f
George Mason - MATH - 214
ffiia,*l*) qnA t/'h d k'Ln;tale iaa= /^'-/l,A/r q* = 2 /&h/a,oeoo/U"=in;t,'a/4^:Or?a4a/ "g&r-rfia,o Cls ( o,att d,rEobcl dt *'=o)nftaotlry haau*ta,4bn = ek/Va-tl'in*L,'lo-f;3;Art* lftVonr V/9 = uwqful./rl#tdQT+Q'k)=otae*at-rhrr
George Mason - MATH - 214
,lAtult2,Lechte 7*-;M,nl)nntt/s, Cuz*9'j?H/-= Vft) 6)IuyltolLV=gvm2 cor-r5'r*'|% )a eo)j'2/tf PH, 3/+)it'tawal f ol <*</A c'l'ldatng t=6r\nrr-'.,A"At &lle ,"S a cuu'?ttt r&.*rq /ry v/o,tf* v h f^t:ry tI^|a/"r' k)i'gX(il = fu,fJ"rtst
George Mason - MATH - 214
t4o*tt,'a,Leofru- 3Lu+ h'n^o:burla.t*V A' t' ar, dtdfL* Lb7/t) ,Vft) ilae. ual,a*-arwa!-ftuoal ls* al^obl .re,t^ c,l tt /t \-ro'u,'a'd-lfrc,il *^*( #rc,/Ell- Jtg,0u'r@.,uL A (e)=oFirc( i^qimaLuze- cetrtrutocrA,-1'=clntetuouul'*gsL<1t2-
George Mason - MATH - 214
!4"n atfC/orr, ('coh'o^ ,lLq*A &u'oIacfw_s'=|Q\(.*h *etrB-q?k-tr*girre.a4Lfu/^ i scfw_alL1E= ecfw_z-"t)il'ldaoee41-.;h'6+"t'"-e ur'nto+u t= LL?gh^a&t-4-exa* &&t' (A -")&'=Cb*t;rt, 141-,'4naTz)il:;+t4o4ttu^'nla?-q 0-4r oLc
George Mason - MATH - 214
l'la;t 2/(.Leocfw_u.e' I aaa+.c\ead orrattl9a raiin gurtte9\ocfw_"*6a'*'ts-oqftr) >o'l" = f (t,fia')YaY-r.f| ?' fbl=orqaI-aPus=o.tfte*e is gtt (aa.*a - 2)th*o ts-+ hL fe44.,fru qtaitctt ,J Ct-tt*"l e*nltfiLas-)2 tn; hal4=+ lfu
George Mason - MATH - 214
kl ,ra e tq.li"r,* tt,La'l+h'u-.Q-:?- sla*e-/ tt"* tf il' , t'W(f"X) G'l +o* P@t'+ q(t)V = oA"-t/tto,fttl^t U2 boqfa,c"Ja Cr, Cz d ac4 ftra*+ (r/, s&tq A^2 / t/f=0sa&'a71.*/ ^"//, .lft)V- ,ttt r. ' ' ^ tt l,-.nr0"+Plt)Y'+ ?tt)A =O)
George Mason - MATH - 214
llon p tq.*-*'-ILe or\^-. /e6r'*r/ = O e Zad a4dr4 L'r,to,t ar",lt coe+/s6+ar"+t^t2 tr2-; c =Q * oAana&o>ish'c ghOil" +, PaAISt)h*rz tea!=)I =('ent *Czerzt4 rr=?z74 ?= 2- if - c^ t^. r hd"?' E =?*',' ut+tev)aatTar'+?r+c=oGrrq&^ ra$.
George Mason - MATH - 214
ItMa-r%Le2/+.r*r*e a 3ad" +'00'* ,? = o :)I@=-Ft)h,*h)u,u?,/,".^*2e4ae1d14,t=r?,%:': '/rea[ 4fi'eh'nct-n -tac*I = sr't acz"tJ) ' ! f/) ,-';, = Fa real r7n.t/C:'1n='tr, ert + co.i"r,ur,": r if ca'*/i42Cte'r nft + C'e?'s'e7tl4
George Mason - MATH - 214
Ltrn 2t(ffi,+plt\, * ?ut= Vft) +o0"nan/uot+, /t) =/ A*, l,an /t) + cfw_ut/*,txlu -J/'-zV = g7 ",- 4v'-3a = o-rt-1,-i-QPort'crrlat s&z-rlbe' /v aaarlaa, 1ia,- ho4luta.* Aont,a@Ur/4 = -/n oAlrn-r,-(t) = C,3=4t/' -3Vh h4. ,!e = hrttt
George Mason - MATH - 214
t-kcfu+eIrlfrd la-ffir.od'"B/'* V =Aft).Lt/atet*;@|r't= Cr e + C, e4t/Aor,t h * tzrea( tubats;nvf= C/(*vt +(>e4, ab*,, t=itt/r Uu<y'e+3)Cu,-, = c,eht + Gterr=4- - rea.l tTeddtr tH = f,/*) +/1"&l :) 4&) = ,!p'Gt + 42,?)If fft),r'qP'fu"
George Mason - MATH - 214
lvloru ttttI.bct*elbftled all;car+ f[ecrt*,'caQ l/r't-ot\ou.alnu, I futq Ku>F;V - rvlcsc Vlur:I trrd =4oLutH=c(o/Free taadat rae/ Ui&-a*aa:Cwr.f=o=o(Inu" +Ku = oFLUh)= eo, ut/o)=4o 'u(t) = C, c* tFt +Eq* raau,t fnn,ktl'r' + K= okr
George Mason - MATH - 214
tti /,VIrbra:h'4:larf a.cfw_?Ie*rn t+lhu" +hl+ kLL:F(qC/'CL(f+o dattpe-lt=o-,lvfrez ,F*o 4*a,*o4sa.l+)-'-=rcLGrrfil'ont f* g*n ,t(Ar'4 t-'(u%aA'o't d/4,to T^t;V)r)I ,Ft =ta;ne' A (eel)ny-'<e unih fftL-l /tuOl rLlLejt;c rt*'-t.r " lt
George Mason - MATH - 214
ftloll.ek,DelLuX"-e, lE .acfw_TqHT = ,-ttf(t)at,\fd*rt,a.3.f"/ f,/ t+',? h/"* fu*+pn(* /rp),b?/"* rror&n 4 /-e rrLffif g4.,'t;/*,>ta)/orrroo@S/*-'>/f".'oen*,v-v. 16) = ttAJ v/,t*c Vftt a^+-n/#t leLr*la.7V/4 ,tna,AJ cfw_oa*"o rl
George Mason - MATH - 214
lvtotl 2/qeertl,r-*cfw_ t.t_.f,(q *J:*'-*fu"r+att4,_(t<cuc ft) =cfw_-.-llr43\/Iu'(t) =cfw_?, t<3cfw_ 7229 4lil - Qsft) =Ql= oua7: *>cc>.o&')n,ba9 &4Qt= /S(o, F3,t<3#f<cfw_l-o, 3 s b<5hzcfw_l-t t>sus*th /t) + 2 us /*) -
George Mason - MATH - 214
zt't ,Lect*e eaI'lAG'ronfk) ,ilt;lo,nY',Fe.Vetu,t4-rt,taho4sfrp loh;\riu'&'Ps aa* a*=cfw_0, tl<t 2'| 2t ) |t<*i' c *=3-! , t2-L.\ J'24 fft) =( o ) +(at-|uirn -+- (r-t)urft)Ln-Br. -rt+1 =f l,olt< +4-t-I o?'tt,qll;nt-,-< +<6
George Mason - MATH - 621
MATH 621, Algebra IAssignment sheet 1Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)Homework to be handed in:(1): Let f : A B and g : B C be functions. Prove the followingimplications:f and g injective g f injec
George Mason - MATH - 621
MATH 621, Algebra IAssignment sheet 2Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)Homework to be handed in:(1): Let G be a group and S G a subset. Show thatC (S ) = cfw_g G : gs = sg for every s S is a subgroup
George Mason - MATH - 621
MATH 621, Algebra IAssignment sheet 3Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)Homework to be handed in:(1):Show that a subgroup of index two of a group is a normal subgroup.(2):Show that the automorphisms
George Mason - MATH - 621
MATH 621, Algebra IAssignment sheet 4Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)Homework to be handed in:(1):A group G is called solvable if there is a normal chain, or sequenceG = G0G1Gn = cfw_e,with each
George Mason - MATH - 621
MATH 621, Algebra IAssignment sheet 5Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)Homework to be handed in:(1):Show that a group G on four elements, |G| = 4 is abelian. Let N4 be thesubset of the symmetric grou
George Mason - MATH - 621
MATH 621, Algebra IAssignment sheet 6Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)Homework to be handed in:(1):Let G be an abelian group with |G| = pn for some n N where p is a primenumber. Show that G has a co
George Mason - MATH - 621
MATH 621, Algebra IAssignment sheet 7Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)Homework to be handed in:(1):Let G be a group with |G| = pn m where p is a prime, gcd(p, m) = 1 andp > m 1. Show that G has a un
George Mason - MATH - 621
MATH 621, Algebra IAssignment sheet 8Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)Homework to be handed in:(1):Let G and H be nite groups of relatively prime orders. Show thatAut(G H ) Aut(G) Aut(H ).=Here Au
George Mason - MATH - 621
MATH 621, Algebra IAssignment sheet 9Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)Homework to be handed in:(1):Let R = cfw_m + n 2 : m, n Z show that R is a subring of R. Showfurther that R (Z2 , +, ) where Z2
George Mason - MATH - 621
MATH 621, Algebra IAssignment sheet 10Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)Homework to be handed in:(1):Let R be an integral domain. If a R is a unit and b R, show there isa unique automorphism of R[X ]
George Mason - MATH - 621
MATH 621, Algebra IAssignment sheet 11Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)Homework to be handed in:(1):For a ring R, the least n N such that n = 1 + + 1 (n times) = 0 iscalled the characteristic of R a
George Mason - MATH - 621
MATH 621 Algebra I Lecture NotesGeir AgnarssonApril 19, 201211.1GroupsSome preliminariesThese lecture notes will follow the class text [1] fairly closely. They are, inpart, based on lectures of the graduate algebra class MATH 250A given bythe lat
George Mason - MATH - 621
/F\/"(,-ttf t'f-PG'-cr$qt\eG;[o,r etcoaret]\Mfrhrrq cfw_tt) i t-r'e G. , @tch Etracha,r Cnra be vieuved aswhere g;eGe fuv eotth t[Cec)ier , GsG. rdz"|'$ ol G."or,r ' i-+u yU-" ( ff bouq, A:Gtu,^p opentl'oq:i)iercfw_(qJ,*r' (t)rqr._(
George Mason - MATH - 621
MATH 621, Algebra ISelected solutions for HW assignment 1Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)(1):Let f : A B and g : B C be functions.(i) Assume that both f and g are injective, we show that g f is also
George Mason - MATH - 621
MATH 621, Algebra ISelected solutions for HW assignment 2Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)(1): Let G be a group and S G a subset. Clearly C (S ) G, so to showthat C (S ) = cfw_g G : gs = sg for every
George Mason - MATH - 621
MATH 621, Algebra ISelected solutions for HW assignment 3Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)(1): Assume that G is a group with a subgroup H of index two in G, so[G : H ] = 2. Let g G. If g H then clearl
George Mason - MATH - 621
MATH 621, Algebra ISelected solutions for HW assignment 4Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)(1):Assume G is a solvable group, so G has a normal chainG = G0G1Gn = cfw_e,(1)where the quotient Gi /Gi1
George Mason - MATH - 621
MATH 621, Algebra ISelected solutions for HW assignment 5Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)(1):Let G be a group on four elements. For each element a G the cyclicsubgroup a is a subgroup of G, and henc
George Mason - MATH - 621
MATH 621, Algebra ISelected solutions for HW assignment 6Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)(1):Let G be an abelian group with |G| = pn for some n N where p is a primenumber. If n = 1 there is nothing
George Mason - MATH - 621
MATH 621, Algebra ISelected solutions for HW assignment 7Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)(1):Let G be a group with |G| = pn m where p is a prime, gcd(p, m) = 1 andp > m 1. If G has N p-Sylow subgrou
George Mason - MATH - 621
MATH 621, Algebra ISelected solutions for HW assignment 8Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)(1):Let G and H be nite groups of relatively prime orders. We want to showthat Aut(G H ) Aut(G) Aut(H ), wher
George Mason - MATH - 621
MATH 621, Algebra ISelected solutions for HW assignment 9Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)(1):Using our more recent notation from class we haveR = cfw_m + n 2 : m, n Z = Z[ 2],all polynomial express
George Mason - MATH - 108
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George Mason - MATH - 108
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George Mason - MATH - 108
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