- 08/26: revision of group actions, Fundamental Counting Principle for orbit size, Lagrange's Theorem
- 08/28: centralizer, normalizer, center of a p-group, existence of Sylow subgroups
- 08/30: Sylow's Theorem, Cauchy's Theorem, free groups, universal mapping property
- 09/04: construction and uniqueness of free groups, rank
- 09/06: presentations, finitely presented groups, word problem
- 09/09: verbal subgroups, varieties and HSP
- 09/11: free groups in varieties, Burnside problem
- 09/13: subnormal series, simple groups, extensions, semidirect product, solvable groups
- 09/16: commutators, derived series, central series, nilpotent groups
- 09/18: upper and lower central series, unitriangular groups
- 09/20: characterizations of nilpotent groups, Fitting subgroup controlling structure of solvable group
- 09/23: Frattini subgroup, Frattini argument, nilpotence of finite Frattini subgroup
- 09/25: Hall pi-subgroups, crossed homomorphisms
- 09/27: Schur-Zassenhaus Theorem, existence and conjugacy of complements
- 09/30: pi-separable groups, existence of Hall pi-subgroups in solvable groups
- 10/02: conjugacy of Hall pi-subgroups in solvable groups, transfer homomorphism
- 10/04: transfer evaluation lemma, transfer into center
- 10/07: transfer into abelian Sylow subgroups
- 10/09: Burnside's normal p-complement theorem, groups with all Sylow subgroups cyclic
- 10/11: group algebras, linear representations of algebras and groups
- 10/14: Maschke's Theorem, Schur's Lemma, irreducible representations of abelian groups
- 10/16: Wedderburn Artin Theorem for semisimple algebras, structure of group algebras over algebraically closed fields
- 10/18: representations of S_3, characters
- 10/21: irreducible characters as basis for class functions over the complex numbers, decomposition of the regular character and of 1
- 10/23: orthogonality relations for characters
- 10/25: character tables
- 10/28: product of characters via tensor products of modules, characters of products of groups
- 10/30: characters are algebraic integers
- 11/01: irreducible character degree divides the group order
- 11/04: nontrivial conjugacy classes in nonabelian simple groups do not have prime power size, Burnside's p^aq^b-Theorem
- 11/06: induced characters, Frobenius reciprocity, Frobenius group defined by complement
- 11/08: existence of Frobenius kernel
- 11/11: group extensions, short exact sequences, equivalence between sequences yield isomorphism between extensions
- 11/13: split extensions, couplings, G-modules, extensions determine factor sets (2-cocyles), Z^2(G,A)
- 11/15: 2-coboundaries B^2(G,A), factor sets determine extensions, equivalence classes of extensions are in bijection with H^2(G,A) = Z^2(G,A)/B^2(G,A)
- 11/18: cochain complexes, projective resolutions, Ext^n(M,D) is independent of choice of projective resolution of M (Dummit-Foote 17.1 Thm 6)
- 11/20: standard resolution of the trivial ZG-module Z
- 11/22: n-cocyles Z^n(G,M), n-coboundaries B^n(G,M) and their quotient H^n(G,M) (n-th cohomology group of G with coefficients in M) and their interpretations
- 12/02: cohomology of Z_m, H^n(G,M) is torsion for finite G
- 12/04: Schur-Zassenhaus Theorem (existence and conjugacy of complements for abelian kernel) via cohomology
- 12/06: talk by Shen Lu
- 12/09: talks by Jordan DuBeau and Robert Green
- 12/11: talks by Michael Wheeler and Lucas Gagnon

- Group actions, Sylow's Theorem [pdf]

- due 09/04 [pdf]
- due 09/11 [pdf]
- due 09/18 [pdf]
- due 09/25 [pdf]
- due 10/02 [pdf]
- due 10/09 [pdf]
- due 10/16 [pdf]
- due 10/23 [pdf]
- due 10/30 [pdf]
- due 11/08 [pdf]
- due 11/13 [pdf]
- due 11/20 [pdf]
- due 12/06 [pdf]

- I. Martin Isaacs. Finite group theory. AMS, 2008.
- Derek J.S. Robinson. A course in the theory of groups. Springer, 2nd edition, 1996.

You can freely download the pdf for the book from Springer through our library via this link - Joseph J. Rotman. An introduction to the theory of groups. Boston : Allyn and Bacon, 3rd edition, 1984.