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math.GR2025

Finite groups, commuting probability, and coprime automorphisms

Eloisa Detomi, Robert M. Guralnick, Marta Morigi +1

Given two subgroups of a finite group , the probability that a pair of random elements from and commutes is denoted by . Suppose that a finite group a…

math.GR2025

Commuting probability for conjugate subgroups of a finite group

Eloisa Detomi, Robert M. Guralnick, Marta Morigi +1

Given two subgroups H,K of a finite group G, the probability that a pair of random elements from H and K commutes is denoted by \pr(H,K). We address the following question. Let P b…

math.GR2025

Groups with a covering condition on commutators

Eloisa Detomi, Marta Morigi, Pavel Shumyatsky

Given a group G and positive integers k,n, we let B_n=B_n(G) denote the set of all elements x in G such that |x^G|\leq n, and we say that G satisfies the (k,n)-covering condition f…

math.GR2024

Commuting probability for the Sylow subgroups of a profinite group

Eloisa Detomi, Marta Morigi, Pavel Shumyatsky

Given two subgroups of a compact group , the probability that a random element of commutes with a random element of is denoted by . We show that if is…

math.GR2024

Commuting probability for approximate subgroups of a finite group

Eloisa Detomi, Marta Morigi, Pavel Shumyatsky

For subsets X,Y of a finite group G, we write Pr(X,Y) for the probability that two random elements x in X and y in Y commute. This paper addresses the relation between the structur…