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 al
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).
Hin
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:
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 recei
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
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
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 s
MATH 3E03 Midterm #2 Solutions
Midterm Test
Duration of test: 50 minutes
McMaster University
November 20, 2015
Matt Valeriote
First Name:
Last Name:
Student No.:
Please answer all five questions. To r
MATH 3E03 Assignment #3
Due: Tuesday, October 27, in class.
1. Find all of the cyclic generators of the group Z20 .
2. Let G be an abelian group and let S = cfw_g G | g 2 = e. Show that
S is a subgrou
MATH 3E03 Assignment #1
Due: Tuesday, September 22, in class. CHANGE: Do not
submit a solution to question #2.
Important note: All work submitted for grading must be your own. You
may discuss homework
MATH 3E03 Assignment #6
Due: Tuesday, December 8, in class
1. List all abelian groups of order 175, up to isomorphism. Show that
every such group has an element of order 35. Does each of these groups
MATH 3E03 Assignment #5
Due: Tuesday, November 24, in class
1. Let G1 and G2 be groups and suppose that H1 is a subgroup of G1 and
H2 is a subgroup of G2 . Show that H1 H2 is a subgroup of G1 G2 .
Fin
MATH 3E03 Assignment #2
Due: Tuesday, October 6, in class.
1. Let G be a group and S a nonempty subset of G. Define the following
relation on G:
a b if and only if ab1 S.
(a) Show that if S is a subgr
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
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
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)
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)
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 =
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
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).
(
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
o
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 student
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 ord
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
o
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
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 al
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
Deadline changed
to Thursday,
November 12, in
class.
MATH 3E03 Assignment #4
Due: Tuesday, November 10, in class.
1. For each pair of groups G and H, determine if they are isomorphic:
(a) G = R , H =
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