Relative cyclic subgroup commutativity degrees of finite groups

Abstract

In this paper we introduce and study the relative cyclic subgroup commutativity degrees of a finite group. We show that there is a finite group with $n$ such degrees for all $n\in\mathbb{N}^*\setminus \lbrace 2\rbrace$ and we indicate some classes of finite groups with few relative cyclic subgroup commutativity degrees. In the end, we prove that the set containing all relative cyclic subgroup commutativity degrees of finite groups is dense in $[0,1].$