A class of finite resistant p-groups

Abstract

A finite p-group P is called resistant if, for any finite group G having P as a Sylow p-group, the normalizer N G (P) controls p-fusion in G. Let P be a central extension as $$1 \to {\mathbb{Z}_{{p^m}}} \to P \to {\mathbb{Z}_p} \times \cdots {\mathbb{Z}_p} \to 1,$$ and |P′| ≤ p, m ≥ 2. The purpose of this paper is to prove that P is resistant.