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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…