Definitions and Theorems
Quiz Date	Definitions/Ideas	Theorems
January 20	group order of a group abelian group binary operation on a set associative operation closure group identity inverse of a group element	To be completed.
January 27	Be able to apply the definitions from January 20. a=b mod n Understand modular arithmetic (for +,-,x) Applications of mod. arith. (dates/time/UPC)	Example 19 on page 48.
February 3	group (This quiz will consist of a proof that a certain set/operation is a group.) general linear groups (Like GL(2,R))	To be completed.
February 10	order of a group order of a group element permutation of a set A symmetric group of degree n even/odd permutations	Theorem 5.4 Theorem 5.5 Theorem 5.6
February 17	subgroup	Theorem 3.3 (Finite Subgroup Test) Theorem 3.1 (One-Step Subgroup Test)
March 3	cyclic subgroup generated by a generator of group G center of a group cyclic group	Theorem 3.4 Theorem 3.5 Theorem 4.3
March 17	cyclic subgroup generated by a generator of group G center of a group cyclic group	Theorem 3.4 Theorem 3.5 Theorem 4.3 Theorem 4.1 and Corollaries Theorem 4.2
March 24	function one-to-one function onto function operation preserving isomorphism	To be completed.
March 31	Same definitions as last week.	Theorem 6.2 Theorem 6.3
April 7	coset of H in G index of H in G	Lemma on pg 135 Lagrange's Thm Corollaries on pg 138
April 21	External direct product	Thm 8.1 Thm 8.2 and Corollaries Thm 11.1 In particular, be able to find all abelian groups of order n.
WEDNESDAY, April 26	normal subgroup	Thm 9.1 Thm 9.5