University of Florida International Conference
Finte Groups 2003*
Opening Lecture
by
Michael Aschbacher
California Institute of Technology
on
"A Question of Farjoun"

Date: Thursday, March 6th, 2003
Room: Reitz Union, Rm 346

 

Conference Inauguration
by
Provost David Colburn: 8:30 am

Lecture: 8:45 am

Refreshments: after the lecture

  Aschbacher PIC

Abstract: Define an embedding of a group H in a group G to be closed, nearly closed, if each homomorphism of H into G, H into H, extends uniquely to a homomorphism of G into G, respectively. As part of his investigation of idempotent augmented fuctors, E. Farjoun posed the following question:


Question 1. If H is a finite closed nilpotent subgroup of a group G, is G=H?

I'll discuss some progress toward an affirmative answer to Farjoun's question in the case of nearly closed subgroups H of finite groups G. In particular the question reduces to the case H a p-group for some prime p, and has an affirmative answer for many classes of p-groups; for example it is true if the nilpotence class of H is at most 3.

Michael Aschbacher is Professor of Mathematics at the California Institute of Technology. He is one of the world's most renowned group theorists who contributed many of the deep theorems which led to the classification of the simple finite groups. Professor Aschbacher is a member of the National Academy of Sciences and was awarded the American Mathematical Society's Cole Prize in 1980. He is the author of a standard reference and several important monographs on finite groups.

 * Finite Groups 2003 is one of the main events in the UF Department of Mathematics Special Year in Algebra 2002-2003. This year was chosen to honor the 70th birthday of our Graduate Research Professor John G. Thompson.

The Special Year in Algebra website is http://www.math.ufl.edu/~sin/ufalgyr/index.html