Limits of Abelian Subgroups of Finitep-Groups

Abstract

Abelian subgroups play a key role in the theory and applications of finite p-groups. Our purpose is to establish some very general results motivated by special results that have been of use. In particular, it is w x known KJ that if a finite p-group, for odd p, has an elementary abelian subgroup of order p, n F 5, then it has a normal elementary abelian subgroup of the same order. Our first main result is a general one of this type.