groups2 - M74 Calm“? (MUN. ‘/2) Usully coins have +wo...

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Unformatted text preview: M74 Calm“? (MUN. ‘/2) Usully coins have +wo sues, had; and fails, 50* i; you via-NE +0 chem-t at coin fun“). You‘ll Ham} 3 coins: HT, HH. “- IMforéadlj, TH i$ 'H‘IQ "same" 05 HT, ;. “were an 3, not '4, coins, This is £25045: +hz your Z; acts on fine sd— 5-? ugh-IsJ «114 “:5 orbits are! {HTaTHL {NHL and iTTL The palf‘i'l' $42? is +0 {I}er 00+ which group is 49”": on 'H‘OSQ. caterinas. Thy, r“? is D.“ 4M. SyMMd'ries oF e szuare. To be precise, L.de +he. wéius as l—l \ _ \ |'\-—-3 THQn Po'l’AHAJ ctodcuksg by (10°35 l 7- 3 ‘l 92(7. 3 “I l . and Hirfhj qpbov-l' ‘Hne Line. T5“ r= (\ i ’31). .76)” Cum-(rij Janet-alias ‘Hu's MIG +0 any Sihafll’p'on where A group “+5 on fie .bJ-uk J: whens-G. Eternal}: SUPPOSQ we cobf ’thc 'er corners of g Sloan with +he colors red MA Hue. How Mom differ“: CoLDN'nJS are five i‘ we atLow +ke swan +0 :4th around? So, For example, an answer -er color-M’s K——B E—-3 l \ amJ \ \ 8’3 R—3 t, be gtuivaten’c. These +uo elemwfs generate. Dc it. Q. 9‘. e‘, t. 193931193. LN X=fou coloring; J- +he szuarel For an ntX and 3.6, x \s etu'wdehi' +0 7x TMrdm, +9 cowl-(- \AQiu‘NMQM' ‘O‘OV'IQSQ’ we UM“ +0 court-V 2232- The. orb“: of 31X is m$(fl=f3x =3¢GL Orbit-Couanj Lew». (aka Bums'dc's lama): Surposc +I-u0. group G ad's on fine. set X. ,Thcn storfits = average 19-Fin ‘Po'nd's = _'_ - ‘6‘ 5:44:04?” when ¥ix(g3=fixex: 3x =x'fl. To Prove, 4465, we infidch a th mre fiohfiioh and 7m“. a “MM. Sumac“. 6 “(rs on 14". set x, The shbzlner, shun o4 xex is defined as shun) =23“. and No+e Hut shun is A why“? of C1. ' Pr“; of The Orbit'Couan Lemma: .7._—— Coniider I Z lFix())l 4%,,”qu z3x=x3 3‘6 = Z_ “hum, . xe‘l~ 31 tht Orb\£- S+&b'\L'\t¢.\' \ 5/9»; m\ = \°'“‘°\. So using Lauren‘st TheoVLM. 7. \or5L‘)‘, # lshktm a.“ +hus l c.“ \S'hub U“ = \orbbm - l Thurm; OrH‘t ' S-Fafio'tu'eer Thcanm'. The. map “mun-93x is o. Nice-Fans have“ G/shbu) and orb (I). Proofi Firs+ ue ms+ st...» +ke. Mp is mil-defiant. Suppose. 3%“th =hsktm, So 3 -. h: «Fa Some 5: £44500. Tm we haw. SK = hsx : hX, So 4410. MG? is utLL-de-Fined. Cum-l7 'H'le MAP is art-h: 'rF yearbb‘), than y=3X in- some 3:6, so 7 is He made of 3 $56). New “"052 33”“!- Then flax-x, 5° 3"}. 6541500, Md 441% 3545600 = Mason. I Mdfina +h'\s Subs'lifvfion yields Md ‘4‘ L = ’— 5; “‘3 é; \orbb‘t“ = mam. Id Now 094! «that each orb“: A - ocwrs (A! times in 'H'i'fi 5W“: So +\'\e 50M- ‘5 «Hue!!!= 0* “Mt?- l | - .— 2 \ele“ '"éfis xZe-Avq X‘)‘ A = 2: 1L‘ ofbfi'i \A\ A s ,, orbits Thucfiore. w- . Z- ”:hdj)‘ =l¢d(¢or5uts ‘ ' a“ Rdvrn'mfl +0 'H'ne. com-0.4 stun-es (gawk, we. see. +kc~+ m. meal {-9 count Find “Pom-W: Lo... «Fier “lotions. Z. Li. Z 3 q i i *8 Thank“. +h¢ numbtr 0; in21v3vattn+ cokorihas '6 49/‘=6. ...
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This note was uploaded on 12/10/2011 for the course MAD 4204 taught by Professor Vetter during the Spring '11 term at University of Florida.

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groups2 - M74 Calm“? (MUN. ‘/2) Usully coins have +wo...

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