On the Schur multiplier of finite 𝑝-groups of maximal class

Abstract

In this article, we prove that the Schur multiplier of a finite 𝑝-group of maximal class of order p n p^{n} ( 4 ≤ n ≤ p + 1 4\leq n\leq p+1 ) is elementary abelian. The case n = p + 1 n=p+1 settles a question raised by Primož Moravec in an earlier article.