Date  Chapter  Description 

Jan 7  1A1B  Introduction, permutation groups 
Jan 9  1B  Permutation group examples 
Jan 11  1C  Definition of group 

Jan 14  1C2A  Isomorphisms, subgroups 
Jan 16  2A  Cyclic groups and their subgroups 
Jan 18  2B  Automorphisms and inner automorphisms 

Jan 21   Martin Luther King Day! (no class) 
Jan 23  2B  Characteristic and normal subgroups 
Jan 25  2C  Commuting subgroups, product counting lemma 

Jan 28  2D  Cosets 
Jan 30  3A  Quotient groups and homomorphisms 
Feb 1  3A  The Isomorphism Theorem 

Feb 4   homework solutions 
Feb 6  3A  The Diamond Theorem and Correspondence Theorem 
Feb 8  3B  Commutator subgroups 

Feb 11  Exam 1 
Feb 13  3C  Simple groups overview 
Feb 15  4A  Group actions  basic definitions 

Feb 18  4A  Group actions  examples, kernels 
Feb 20  4B  Group actions  orbits and transitivity 
Feb 22  4C  The OrbitStabilizer theorem and Finite Counting Principle 

Feb 25  4C  Product Counting Lemma, Cauchy's Theorem 
Feb 27  5A  The Sylow E Theorem 
Mar 1  5A  The Sylow DC Theorems 

Mar 4  5A  The Sylow C Theorem and the # of Sylow psubgroups 
Mar 6  5A  The Sylow Counting Theorem (mod p) 
Mar 8  5B  Nonsimplicity of groups of order p^{2}q, p^{3}q 

Mar 11   Spring Break! (no class) 
Mar 13   Spring Break! (no class) 
Mar 15   Spring Break! (no class) 

Mar 18  5B  More nonsimplicity of groups of certain orders 
Mar 20  5C  pgroups have big centers 
Mar 22  5C  Normalizers grow in pgroups 

Mar 25  6A  Symmetric groups  notations 
Mar 27  Exam 2 
Mar 29   Religious holiday! (no class) 

Apr 1  6A  Symmetric groups  conjugation 
Apr 3  6B  Centers of symmetric groups 
Apr 5  6B, handout  Alternating groups  welldefinedness 

Apr 8  6C  Alternating groups are simple 
Apr 10  7A  Direct products 
Apr 12  7A  Relation between internal/external direct products 

Apr 15  7A  Minimal normal subgroups 
Apr 17  7C  Semidirect products  motivation and warmup 
Apr 19  7C  Semidirect products are welldefined; conjugation 

Apr 22  7C  Relation between internal/external semidirect products 
Apr 24   Fundamental Theorem of Abelian Groups; PSL(2,7) is simple 

Apr 29  Final exam (12:00  3:00pm) 