Abstract

We study the number of elements x and y of a finite group G such that x⊗y=1G⊗G in the nonabelian tensor square G⊗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.