**Department of Mathematics**

**"To Make Finite Group Theory More of a Calculus,
Part I"**

By

** Abstract:** The category of groups
and their exomorphisms is nicer than the category of
groups and their homomorphisms. It is obtained by quotienting out modulo inner automorphisms.
After making that simplification, we shall discuss the three group isomorphism
theorems. For some contexts in finite group theory, it is helpful to consider a
category containing two mutually opposite copies of the category of exomorphisms. The two kinds of exomorphisms
are related by a formula called the Mackey Formula. In a later seminar, we
shall indicate something of this new approach to the theory of group functors;
and a richer formalism involving further structures and formulas. This first
seminar, though, is intended just as an introductory illustration of the proper
use of category language: ideological influence. There will be no
"category theory", no general results about categories; we shall need
to review only the notion of a category and the concept of a representation of
one category within another category.

**Date: ****Thursday, September 26, 2012**

**Time: ****15.40-16.30**

**Place: ****Mathematics Seminar Room,
SA-141**

**All are most cordially invited.
Tea and cookies will be served before the talk.**