MATH 3020 A: Homework 10
SOLUTION IDEAS
To submit, use the assignment box for the course which is across from the North 5th oor Ross
elevators. Late homework will not be accepted.
Solve the following. Carefully justify any statements you make.
1. Prove di
MATH 3020 A: Homework 6
Solution Ideas
1. Give a careful and detailed proof of
Theorem 6.5: For every positive integer n, Aut(Zn ) is isomorphic to U (n).
You may use the proof sketch in the text as a starting point.
Following the text, dene a mapping Aut
MATH 3020 A: Homework 5
Solution Ideas
1. (Herstein) Prove that the smallest subgroup of Sn containing (1, 2) and (1, 2, . . . , n) is Sn .
Suggestion: To obtain some insight, study the case n = 4.
SOLUTION IDEA
As Sn is generated by transpositions, it su
MATH 3020 A: Homework 4
Soution Ideas
Herstein, in Topics in Algebra poses the following exercise.
Let G be a nite abelian group in which the number of solutions in G of the equation
xk = e is at most k for every positive integer k . Prove that G must be
MATH 3020 A: Homework 2
Solution Ideas
Solve the following. Carefully justify any statements you make.
1. (a) Prove that if a is a divisor of bc and gcd(a, b) = 1, then a is a divisor of c.
(b) If a is a divisor of x and b is a divisor of x and gcd(a, b)
S OL U Tfo t-J
MAT H 3020 A: H omework 3
Du e F r iday Oct ober 12 a t No on
To s ub m it , use the assign me nt box for t h e course which is across from the Nort h 5 t h floor Ross
elevators. Late homewo rk will n ot b e a ccepted .
So l ve t he follo
MATH 3020 A: Homework 7
Solution Ideas
1. Give a careful and detailed proof of the rst part of
Theorem 8.3: Suppose s and t are relatively prime. Then U(st) is isomorphic to the external
direct product of U(s) and U(t). In short,
U (st) U (s) U (t) .
You
MATH 3020 A: Homework 8
SOLUTION IDEAS
To submit, use the assignment box for the course which is across from the North 5th oor Ross
elevators. Late homework will not be accepted.
1. Up to isomorphism, there are three abelian groups of order 8.
(a) Identif
York University
Faculty of Science and Engineering
Math 3020 A
Class Test 3
SOLUTIONS
Instructions:
1. Time allowed: 50 minutes.
2. Calculators are not permitted.
NO INTERNET CONNECTED DEVICES OR OTHER AIDS PERMITTED
3. Show your work. Your work must just
York University
Faculty of Science and Engineering
Math 3020 A
Class Test 4
SOLUTIONS
Instructions:
1. Time allowed: 80 minutes.
2. Calculators are not permitted.
NO INTERNET CONNECTED DEVICES OR OTHER AIDS PERMITTED
3. Show your work. Your work must just
York University
Faculty of Science and Engineering
Math 3020 A
Class Test 2
SOLUTIONS
Instructions:
1. Time allowed: 50 minutes.
2. Calculators are not permitted.
NO INTERNET CONNECTED DEVICES OR OTHER AIDS PERMITTED
3. Show your work. Your work must just
York University
Faculty of Science and Engineering
Math 3020 A
Class Test 1
SOLUTION IDEAS
Instructions:
1. Time allowed: 50 minutes.
2. Calculators are not permitted.
NO INTERNET CONNECTED DEVICES OR OTHER AIDS PERMITTED
3. Show your work. Your work must
MATH 3020 A: Homework 9
SOLUTION IDEAS
To submit, use the assignment box for the course which is across from the North 5th oor Ross
elevators. Late homework will not be accepted.
Solve the following. Carefully justify any statements you make.
1. (Herstein
MATH 3020 A: Homework 1
Solution Ideas
Solve the following. Carefully justify any statements you make.
1. Let S be a set and let 2S be the set whose elements are the various subsets of S . In 2S dene
and addition and multiplication as follows: If A, B 2S