Powerful actions and non-abelian tensor products of powerful p-groups

Abstract

We introduce the notion of a powerful action of a p-group upon another p-group. This represents a generalization of powerful p-groups introduced by Lubotzky and Mann in 1987. We derive some properties of powerful actions and study faithful powerful actions. We also prove that the non-abelian tensor product of powerful p-groups acting powerfully and compatibly upon each other is again a powerful p-group.