Considerations on the subgroup commutativity degree and related notions

Abstract

The concept of subgroup commutativity degree of a finite group $G$ is arising interest in several areas of group theory in the last years, since it gives a measure of the probability that a randomly picked pair $(H,K)$ of subgroups of $G$ satisfies the condition $HK=KH$. In this paper, a stronger notion is studied and relations with the commutativity degree are found.

13 pages; this is a complete new version, entirely rewritten: inaccuracies were found and there was the desire to cover more substantially the large literature which is growing in this field in the last years

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Cited by in corpus (2)

• Commuting probability and simultaneous conjugacy classes of commuting tuples in a group
• Factorization number and subgroup commutativity degree via spectral invariants