Rendiconti del Seminario Matematico della Università di Padova


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Volume 139, 2018, pp. 225–240
DOI: 10.4171/RSMUP/139-9

Published online: 2018-06-06

Cyclic subgroup commutativity degrees of finite groups

Marius Tărnăuceanu[1] and Mihai-Silviu Lazorec[2]

(1) University “Al. I. Cuza”, Iasi, Romania
(2) University “Al. I. Cuza”, Iasi, Romania

In this paper we introduce and study the concept of cyclic subgroup commutativity degree of a finite group $G$. This quantity measures the probability of two random cyclic subgroups of $G$ commuting. Explicit formulas are obtained for some particular classes of groups. Acriterion for a finite group to be an Iwasawa group is also presented.

Keywords: Cyclic subgroup commutativity degree, subgroup commutativity degree, poset of cyclic subgroups, subgroup lattice

Tărnăuceanu Marius, Lazorec Mihai-Silviu: Cyclic subgroup commutativity degrees of finite groups. Rend. Sem. Mat. Univ. Padova 139 (2018), 225-240. doi: 10.4171/RSMUP/139-9