On commuting probabilities in finite groups and rings
Copyright policy )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.
9 pages
- University of Technology Russian Federation
annihilating probability, Nil and nilpotent radicals, sets, ideals, associative rings, finite ring, commuting probability, Mühendislik, Mathematics - Rings and Algebras, Engineering, nilpotent group, Rings and Algebras (math.RA), Finite nilpotent groups, \(p\)-groups, finite group, Finite group;Finite ring;Commuting probability;Annihilating probability;Nilpotent group;Nilpotent ring, Probabilistic methods in group theory, nilpotent ring, FOS: Mathematics, Generalizations of commutativity (associative rings and algebras), Primary: 16U80, Secondary: 05C25, 20P05, 16N40, 20D15
annihilating probability, Nil and nilpotent radicals, sets, ideals, associative rings, finite ring, commuting probability, Mühendislik, Mathematics - Rings and Algebras, Engineering, nilpotent group, Rings and Algebras (math.RA), Finite nilpotent groups, \(p\)-groups, finite group, Finite group;Finite ring;Commuting probability;Annihilating probability;Nilpotent group;Nilpotent ring, Probabilistic methods in group theory, nilpotent ring, FOS: Mathematics, Generalizations of commutativity (associative rings and algebras), Primary: 16U80, Secondary: 05C25, 20P05, 16N40, 20D15
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