The Schur Multipliers of $p$-Groups of Order $p^5$

TL;DR

This paper computes the Schur multipliers, non-abelian tensor squares, and exterior squares of non-abelian p-groups of order p^5, and determines their capability, advancing understanding of their algebraic structure.

Contribution

It provides explicit calculations of Schur multipliers and related invariants for p-groups of order p^5, and classifies their capability, a novel contribution in this area.

Findings

Explicit formulas for Schur multipliers of p^5 groups

Classification of capable groups of order p^5

Enhanced understanding of p-group structure

Abstract

In this article, we compute the Schur multiplier, non-abelian tensor square and exterior square of non-abelian $p$-groups of order $p^5$. As an application we determine the capability of groups of order $p^5$.