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2019/94/1-2 (9) — DOI: 10.5486/PMD.2019.8290 — pp. 157-169

Finite groups with two relative subgroup commutativity degrees

Authors: Mihai-Silviu Lazorec and Marius Tărnăuceanu

Abstract:

In this paper, we show that there is an infinite number of finite groups with two relative subgroup commutativity degrees. Also, we indicate a sufficient condition such that a finite group has at least three relative subgroup commutativity degrees, and we prove that $D_6$ is the only finite dihedral group with two relative subgroup commutativity degrees. Finally, we study the density of the set containing all relative subgroup commutativity degrees of finite groups.

Keywords: subgroup commutativity degree, relative subgroup commutativity degree, subgroup lattice

Mathematics Subject Classification: 20D60, 20P05, 20D30, 20E45