Department of Mathematics

BILKENT ALGEBRA SEMINAR

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

By

LAURENCE BARKER

(Bilkent University)

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.