the textit{commutativity degree}, $pr(g)$, of a finite group $g$ (i.e. the probability that two (randomly chosen) elements of $g$ commute with respect to its operation)) has been studied well by many authors. it is well-known that the best upper bound for $pr(g)$ is $frac{5}{8}$ for a finite non--abelian group $g$. in this paper, we will define the same concept for a finite non--abelian textit{...

The study of honest elementary degrees has its roots in subrecursion theory from the nineteen seventies. Some relevant papers are Meyer & Ritchie [12] and Machtey [9–11]. These papers deal with subrecursive function classes being generated by so-called honest functions where an honest function is defined relative to a subrecursive class S and a model of computation: a function f : N → N is hone...