On commuting probabilities in finite groups and rings

2020/10/02 by Juráš, Martin, Ursul, Mihail
#16N40 #20D15 #20P05 #FOS: Mathematics #Primary: 16U80 #Rings and Algebras (math.RA) #Secondary: 05C25

paper · doi:10.48550/arxiv.2010.01188

Abstract

We show that the set of all commuting probabilities in finite rings is a subset of the set of all commuting probabilities in finite nilpotent groups of class ≤2. We believe that these two sets are equal; we prove they are equal, when restricted to groups and rings with odd number of elements.

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