Cornell Math - MATH 732, Spring 2007

MATH 732: Topics in Group Theory (Spring 2007)

Instructor: R. Keith Dennis

Meeting Time & Room

Prerequisites: Basics of algebra, in particular group theory (e.g., MATH 434, MATH 631, or MATH 632)

Text: None. Several references might be useful: e.g.

  • K. Brown, Cohomology of Groups, Springer.
  • M. Hall, The Theory of Groups, MacMillan.
  • H. Kurzweil and B. Stellmacher, The Theory of Finite Groups, Springer.
  • H. Neumann, Varieties of Groups, Springer.
  • J. Rotman, An Introduction to the Theory of Groups, Springer.
  • M. Suzuki, Group Theory I, II, Springer.

Likely topics to be covered:

  1. Universal properties. Exact sequences of groups, split extensions, direct products, central products. semi-direct products, wreath products, cocycles, second cohomology group.
  2. Schur-Zassenhaus Theorem.
  3. Wedderburn-Krull-Remak-Schmidt Theorem.
  4. Hall's theorems on solvable groups.
  5. The Moebius function of finite groups.
  6. Varieties of groups.

Topics (other than the first 2) will not necessarily be covered in this order; other topics are possible - make a request.