On the Schur Multiplier of finite $p$-groups of maximal class

TL;DR

This paper proves that the Schur Multiplier of certain finite p-groups of maximal class is elementary abelian, resolving a specific case of a previously posed question and advancing understanding of their algebraic structure.

Contribution

It establishes that the Schur Multiplier of finite p-groups of maximal class with order between p^4 and p^{p+1} is elementary abelian, including a key case resolving an open question.

Findings

Schur Multiplier is elementary abelian for these groups

The case n = p+1 confirms a conjecture by Moravec

Advances classification of 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 $p^n ~(4 \leq n \leq p+1)$ is elementary abelian. The case $n = p+1$ settles a question raised by Primo\v{z} Moravec in an earlier article.