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Ryerson University - MTH 617 Assignment 7, W2015
Date due: Monday, April 06, 2015
Question 1 Let G be a group with |G| = 125. Let C denote the center of G.
Show that either G/C or G is abelian.
Question 2 Compete the following steps to prove the followi

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Ryerson University - MTH 617 Assignment 6, W2015
Date due: Monday, March 30rd, 2015
Question 1 Let G be a group. For a, b in G, we write a b if b = xax1 for
some x G. Then its easy to verify that is an equivalence relation on G.
The equivalence class of

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Ryerson University - MTH 617 midterm cheat sheet
Terminologies and some results proved in classes
Let G be a group with the identity denoted by e. Let a G. Let k, l be
integers (negative, 0 or positive).
1. Then ak al = ak+l and (ak )l = akl .
2. < a >:

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Ryerson University - MTH 617 Final Exam
15:00 -18:00, ENG 106; April 22, 2015.
Instructions: Do not ask for any interpretation of any questions below.
Attempt every part of the next question. Five points for each part.
Question 1
1. Let G be a group and

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Ryerson University - MTH 617 Assignment 4, W2015
Date due: Wednesday, March 12th, 2015
Question 1 Let G be a group and let a be any element of G. Let n, k be
positive integers. Assume that ord(a) = n and gcd(n, k) = d. Show that
ord(ak ) =
n
.
d
Hint: U

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Ryerson University - MTH 617 Assignment 3
Date due: Monday, Feb 23rd
Question 1 Let a, b be elements in a group and assume that they both
have finite orders, m and n, respectively. If m and n are relatively prime
(that is, m and n have no factors in com

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Ryerson University - MTH 617 (Winter 2015) Assignment 1
Date due: 1pm, Tuesday, Jan 27.
Question 1 Let G :=
ordinary multiplication.
n
1+2m
1+2n
o
: m, n Z . Show that G is a group under
Question 2 Let a, b, c be elements in a group G. If abc is its own

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Ryerson University - MTH 617 Assignment 2
Date due: 1pm, Feb 3rd
Question 1 consider the group Z12 .
1. List all elements of order (a) 2 (b) 3 (c) 4.
2. Find all of its subgroups.
Question 2 Let G be a group and let a G with ord(a) < .
1. If n is any in

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Ryerson University - MTH 617 Assignment 5, W2015
Date due: Monday, March 23rd, 2015
Question 1 Let G be a group and let H B G. Then G/H is cyclic if and only
if there is some a G with the following property: For each x G, there is
some integer n such th