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. Using this new concept, we are able to show that the set containing all cyclic subgroup commutativity degrees of finite groups is not dense in $[0, 1]$.