Probabilistic aspects of ZM-groups

Abstract

In this paper we study probabilistic aspects such as the (cyclic) subgroup commutativity degree and different types of factorization numbers of ZM-groups. We show that these quantities can be computed using the sizes of the conjugacy classes of these groups. In the end, we point out a class of groups whose (cyclic) subgroup commutativity degree vanishes asymptotically.

Keywords:

• Cyclic factorization number
• cyclic subgroup commutativity degree
• factorization number
• number of maximal factorizations
• subgroup commutativity degree

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 20D60
• 20P05
• Secondary 20D30
• 20E28
• 20F16

Acknowledgements

The author is grateful to the reviewer for its remarks which improve the previous version of the article.