MATH 7390 - Topics in Finite Group Theory

Keith Dennis, spring 2017.

Prerequisites: MATH 4340 and/or MATH 6310

This should be understandable to beginning grad students.

Theorems dealing with the structure and properties of finite groups will be developed using the basic ideas of representation theory: i.e., combining results from basic linear algebra with elementary group theory to obtain sophisticated results in group theory. Prerequisites will be developed as needed.

If there is interest, the ideas can be supplemented with computational aspects using the computer algebra systems GAP and/or Magma.

Some topics likely to be appear are

• Permutation Representations
• Characters
• Character Tables
• The Burnside ring