MATH 3E03 Midterm #2 Solutions
Matt Valeriote
Midterm Test
Duration of test: 60 minutes
McMaster University
November 19, 2014
First Name:
Last Name:
Student No.:
Please answer all ve questions. For all questions, write your answers up in
the answer bookle
MATH 3E03 Assignment #6 Solutions
Due: Thursday, November 29, in class
1. Suppose that H and K are normal subgroups of the group G such that
G = HK. Show that G/(H K) is isomorphic to (G/H) (G/K).
Hint: Use the First Isomorphism Theorem after rst nding a
MATH 3E03 Assignment #4 Solutions
Due: Monday, November 10, in class
1. Let H1 , H2 , K1 , and K2 be groups such that H1 is isomorphic to K1 and
H2 is isomorphic to K2 . Show that H1 H2 is isomorphic to K1 K2 .
Solution: Since Hi is isomorphic to Ki , for
MATH 3E03 Assignment #3 Solutions
Due: Monday, October 20, in class
1. For each pair of group G and subgroup H, describe the left and right
cosets of H in G and nd [G : H]:
(a) G = Q, H = Z.
Solution: Each coset of Z in Q is of the form q + Z for some
rat
MATH 3E03 Midterm #1 SOLUTIONS
Matt Valeriote
Midterm Test
Duration of test: 60 minutes
McMaster University
October 24, 2014
Initials:
Last Name:
Student No.:
Please answer all six questions. To receive full credit, provide justications
for your answers.
A statement in logic or mathematics is an assertion that is either true or false.
A mathematical proof is nothing more than a convincing argument about the accuracy of
a statement
A statement could be as simple as \10=5 = 2"
However, mathematicians are us
MATH 3E03 Assignment #5 Solutions
Due: Monday, November 17, in class
Important note: All work submitted for grading must be your own. You
may discuss homework problems and related material with other students,
but you must not submit work copied from othe
MATH 3E03 Assignment #6 Solutions
Due: Monday, December 1, in class
Important note: All work submitted for grading must be your own. You
may discuss homework problems and related material with other students,
but you must not submit work copied from other
Please wait.
If this message is not eventually replaced by the proper contents of the document, your PDF
viewer may not be able to display this type of document.
You can upgrade to the latest version of Adobe Reader for Windows, Mac, or Linux by
visiting
The Prince Philip Movement is a religious cult from an island of Vanuatu, which is located at 1700km east from Autralia. The followers of this cult, the Yaohnanen tribe from Tanna island, believe that Prince Philip, Duke of Edinburgh, the consort of Queen
MATH 3E03 Assignment #1 Solutions
Due: Monday, September 22, in class
Important note: All work submitted for grading must be your own. You
may discuss homework problems and related material with other students,
but you must not submit work copied from oth
MATH 3E03 Assignment #2 Solutions
Due: Monday, October 6, in class
1. Let G be a group with group operation and let c G be an element
of G. For this choice of c, dene to be the following operation on G:
for x, y G,
x y =xcy
where the product on the right
MATH 3E03 Midterm #2 Solutions
Matt Valeriote
Midterm Test
Duration of test: 60 minutes
McMaster University
November 19, 2013
First Name:
Last Name:
Student No.:
Please answer all ve questions. For all questions, write your answers up in
the answer bookle
Note: In the
original version,
this was 96.
MATH 3E03 Assignment #6
Due: Thursday, November 29, in class
1. Suppose that H and K are normal subgroups of the group G such that
G = HK. Show that G/(H K) is isomorphic to (G/H) (G/K).
Hint: Use the First Isom
MATH 3E03 Assignment #5 Solutions
Due: Thursday, November 1, in class
1. For each group G and subset H, determine if H is a normal subgroup
of G:
(a) G = A4 , H = cfw_(1), (12)(34), (13)(24), (14)(23).
Solution: Since |A4 | = 12 and |H| = 4, then H has th
MATH 3E03 Assignment #5
Due: Thursday, November 1, in class
1. For each group G and subset H, determine if H is a normal subgroup
of G:
(a) G = A4 , H = cfw_(1), (12)(34), (13)(24), (14)(23).
(b) G = D4 , H = cfw_id, s.
(c) G = GL4 (R), H = SL4 (R).
2. De
MATH 3E03 Assignment #4
Due: Thursday, October 25, in class
1. For each pair of groups G and H, determine if they are isomorphic:
(a) G = Q, H = C.
Solution: Since the cardinality of Q is smaller than the cardinality
of C (Q is countably innite while C is
MATH 3E03 Assignment #4
Due: Thursday, October 25, in class
1. For each pair of groups G and H, determine if they are isomorphic:
(a) G = Q, H = C.
(b) G = U (10), H = U (12).
(c) G = Z, H = M3 (Z).
(d) G = Z15 and H = Z3 Z5 .
2. Show that there are exact
MATH 3E03 Assignment #2
Due: Thursday, October 4, in class
NOTE: A Graduate Studies Information Session will be held on Wednesday,
3 October, 4:30pm in HH217.
1. Let G = Z Z. Dene a binary operation
on G as follows:
(a, b) (c, d) = (a + c, (1)c b + d).
(a
MATH 3E03 Assignment #1
Due: Thursday, September 20, in class
Important note: All work submitted for grading must be your own. You
may discuss homework problems and related material with other students,
but you must not submit work copied from others.
1.
MATH 3E03 Assignment #3 Solutions
Due: Thursday, October 11, in class
1. Give an example of a group of order 60 that is not abelian, and an
element from that group that has order 5. Can a group of order 60
have an element of order 8?
Solution: The dihedra
MATH 3E03 Assignment #2
Due: Thursday, October 4, in class
NOTE: A Graduate Studies Information Session will be held on Wednesday,
3 October, 4:30pm in HH217.
1. Let G = Z Z. Dene a binary operation
on G as follows:
(a, b) (c, d) = (a + c, (1)c b + d).
(a
MATH 3E03 Assignment #3
Due: Thursday, October 11, in class
1. Give an example of a group of order 60 that is not abelian, and an
element from that group that has order 5. Can a group of order 60
have an element of order 8?
2. Let H and K be subgroups of
1. Intrati in contul de admin din Oracle SQL si executati
scriptul create_user. Acesta va elimina userul student
creat in semestrul trecut (daca exista) si va crea altul
cu mai mult spatiu de stocare pe disc.
2. Executati scriptul import.bat (trebuie sa f
Abstract Algebra
Theory and Applications
Abstract Algebra
Theory and Applications
Thomas W. Judson
Stephen F. Austin State University
Sage Exercises for Abstract Algebra
Robert A. Beezer
University of Puget Sound
August 9, 2016
Website: abstract.pugetsoun