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On the tensor degree of finite groups
We study the number of elements and of a finite group such that
in the nonabelian tensor square
of . This number, divided by , is called the tensor degree of 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