On commuting probabilities in finite groups and rings

Year 2022, , 9 - 15, 15.01.2022

Martin Juras Mihail Ursul

https://doi.org/10.13069/jacodesmath.1056492

Abstract

We show that the set of all commuting probabilities in finite rings is a subset ofthe set of all commuting probabilities in finite nilpotent groups of class $\leq 2$. These two sets are equal when restricted to groups and rings with odd number of elements.

Keywords

Finite group, Finite ring, Commuting probability, Annihilating probability, Nilpotent group, Nilpotent ring

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