MA 4163/6163 - Schedule


Schedule of topics: MA 4163/6163

Date Chapter       Description 
Jan 7           1A-1B Introduction, permutation groups
Jan 9 1B Permutation group examples
Jan 11 1C Definition of group

Jan 14 1C-2A 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 Orbit-Stabilizer 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 D-C Theorems

Mar 4 5A The Sylow C Theorem and the # of Sylow p-subgroups
Mar 6 5A The Sylow Counting Theorem (mod p)
Mar 8 5B Nonsimplicity of groups of order p2q, p3q

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 p-groups have big centers
Mar 22 5C Normalizers grow in p-groups

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 -- well-definedness

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 well-defined; 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)