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.Comment: 10 pages, accepted in Ars Combinatoria with revision