The Non-Abelian Tensor Square and Schur multiplier of Groups of Orders $p^2q$, $pq^2$ and $p^2qr$

TL;DR

This paper computes the non-abelian tensor square and Schur multiplier for specific classes of finite groups with orders involving products of primes, expanding understanding of their algebraic structure.

Contribution

It provides explicit calculations of the non-abelian tensor square and Schur multiplier for groups of orders $p^2q$, $pq^2$, and $p^2qr$, which were previously not fully characterized.

Findings

Determined the non-abelian tensor square for groups of orders $p^2q$, $pq^2$, and $p^2qr$.

Computed the Schur multiplier for these classes of groups.

Extended the classification of these invariants for groups of square-free and prime power order.

Abstract

The aim of this paper is to determine the non-abelian tensor square and Schur multiplier of groups of square free order and of groups of orders $p^2q$, $pq^2$ and $p^2qr$, where $p$, $q$ and $r$ are primes and $p<q<r$.