Rendiconti del Seminario Matematico della Università di Padova
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Published online: 2018-06-06
Cyclic subgroup commutativity degrees of finite groupsMarius Tărnăuceanu and Mihai-Silviu Lazorec (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