On commuting probabilities in finite groups and rings

On commuting probabilities in finite groups and rings

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 \(\le2\). 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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Veröffentlicht in:arXiv.org 2020-10
Hauptverfasser: Juráš, Martin, Ursul, Mihail
Format: Artikel
Sprache:eng
Schlagworte:
Commuting
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Zusammenfassung: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 \(\le2\). We believe that these two sets are equal; we prove they are equal, when restricted to groups and rings with odd number of elements.
ISSN:2331-8422