On a result of Johnson about Schur multipliers

Abstract

The purpose of this short note is to give a new and shorter proof of the following theorem of Johnson [1], and to extend it somewhat.Theorem 1. Let G be a finite non-cyclic p-group possessing a non-empty subset X such that, for each x in X, <X/{x}>G′ is a complement for <x> in G. Then the Schur multiplier of G is non-trivial.