A note on the invariance in the nonabelian tensor product

TL;DR

This paper investigates conditions under which properties of groups are preserved in their nonabelian tensor product, expanding understanding of invariance in this algebraic construction.

Contribution

It identifies weak conditions that ensure properties pass from groups to their nonabelian tensor product, broadening the scope of invariance results.

Findings

Properties pass from groups to tensor products under certain conditions

Weak conditions for property transfer are characterized

The study extends known invariance results in nonabelian tensor products

Abstract

In the nonabelian tensor product $G\otimes H$ of two groups $G$ and $H$ many properties pass from $G$ and $H$ to $G\otimes H$. There is a wide literature for different properties involved in this passage. We look at weak conditions for which such a passage may happen.