Cyclicity degrees of finite groups

Abstract

We introduce and study the concept of cyclicity degree of a finite group $G$. This quantity measures the probability of a random subgroup of $G$ to be cyclic. Explicit formulas are obtained for some particular classes of finite groups. An asymptotic formula and several minimality/maximality results on cyclicity degrees are also inferred.

19 pages, revised. arXiv admin note: text overlap with arXiv:1312.1427

References in corpus (2)

• On the number of cyclic subgroups of a finite abelian group
• On the subgroups of finite Abelian groups of rank three