On the tensor degree of finite groups

Abstract

We study the number of elements $x$ and $y$ of a finite group $G$ such that $x\otimes y=1_{{}_{G\otimes G}}$ in the nonabelian tensor square $G\otimes G$ of $G$. This number, divided by $|G{|}^2$, is called the tensor degree of $G$ and has connection with the exterior degree, introduced few years ago in [P. Niroomand and R. Rezaei, On the exterior degree of finite groups, Comm. Algebra 39 (2011), 335--343]. The analysis of upper and lower bounds of the tensor degree allows us to find interesting structural restrictions for the whole group.

10 pages, accepted in Ars Combinatoria with revisions

Cited by in corpus (1)

• Considerations on the subgroup commutativity degree and related notions