# Abelian quotient groups of finite groups

Seminar
Speaker
George Glauberman (University of Chicago)
Date
28/08/2022 - 13:00 - 12:00Add to Calendar 2022-08-28 12:00:00 2022-08-28 13:00:00 Abelian quotient groups of finite groups Suppose S is a non-identity Sylow p-subgroup of a finite group G and H is the normalizer of S in G. A classic theorem of Burnside asserts that if S is abelian, then G has a normal p-complement if and only if H has a normal p-complement. More generally, G has a normal subgroup with a quotient group of order p if and only if H has one; in this case, G is not a non-abelian simple group. There are analogous results in which p > 3, S is an arbitrary p-group, and H is replaced by the normalizer of some non-identity characteristic subgroup of S. In this talk, we plan to discuss some new related results and open problems for p > 3 as well as for p = 3. https://us02web.zoom.us/j/87856132062 Meeting ID: 878 5613 2062 Third floor seminar room, Mathematics building, and on Zoom. See link below. אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Third floor seminar room, Mathematics building, and on Zoom. See link below.
Abstract

Suppose S is a non-identity Sylow p-subgroup of a finite group G and H is the normalizer of S in G. A classic theorem of Burnside asserts that if S is abelian, then G has a normal p-complement if and only if H has a normal p-complement. More generally, G has a normal subgroup with a quotient group of order p if and only if H has one; in this case, G is not a non-abelian simple group. There are analogous results in which p > 3, S is an arbitrary p-group, and H is replaced by the normalizer of some non-identity characteristic subgroup of S. In this talk, we plan to discuss some new related results and open problems for p > 3 as well as for p = 3.

https://us02web.zoom.us/j/87856132062

Meeting ID: 878 5613 2062

Last Updated Date : 16/08/2022