Math 223: Abstract Algebra
Homework 4 Additional Problems
Prof. Matthew Moore
Due: 2014-09-18
1. Let H and G be two nite groups. Show that there is a third group, A that contains subgroups isomorphic
to G and H.
2. Consider the alternating group as a subg
Math 223: Abstract Algebra
Homework 3 Additional Problems
Prof. Matthew Moore
Due: 2014-09-11
Modied: September 9, 2014
1. Deleted
2. Find a generating set for S4 .
3. Deleted
4. Find a generating set for Sn for n N.
5. Deleted
1
Math 223: Abstract Algebra
Homework 1 Additional Problems
Prof. Matthew Moore
Due: 2014-08-28
1. Show that each of the following sets have the same cardinality as N, the set of natural numbers. [Hint:
If there is an injective function : A B then |A| |B|.]
Math 223: Abstract Algebra
Homework 2 Additional Problems
Prof. Matthew Moore
Due: 2014-09-04
1. Let G = G; be a nite monoid with binary operation . For a, b G, prove that if a and a b are
invertible then b is invertible as well.
2. Let G be a nite semigr
Math 224: Quiz 2
2014-09-02
Name:
Dene each of the following.
1. binary operation
Solution: A binary operation on a set S is a function : S S S.
2. monoid
Solution: A monoid is a semigroup S; where S contains an identity element for .
3. semigroup
Solutio
Math 223: Quiz 1
2014-08-26
Name:
Dene each of the following.
1. power set
Solution: If S is a set then the power set of S is P(S) = cfw_X | X S.
2. injective (one-to-one)
Solution: If f : A B is a function, then f is injective if for all a, b A f (a) = f
Math 223: Quiz 3
2014-09-09
Name:
Dene each of the following.
1. cyclic group
Solution: A cyclic group is a group G such that G = g for some g G.
2. generator of a group
Solution: A generator of a group G is an element g G such that G = g .
3. subgroup
So