Compatible actions and non-abelian tensor products

TL;DR

This paper investigates the structure of non-abelian tensor products of groups under compatible actions, expanding understanding of their algebraic properties and potential applications.

Contribution

It introduces a framework for compatible actions of groups and explores the resulting non-abelian tensor products, providing new insights into their algebraic structure.

Findings

Characterization of compatible actions for group pairs

Conditions for the existence of non-abelian tensor products

Structural properties of the tensor products studied

Abstract

For a pair of groups $G, H$ we study pairs of actions $G$ on $H$ and $H$ on $G$ such that these pairs are compatible and non-abelian tensor products $G \otimes H$ are defined.