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