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.
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