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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…
math.GR2024
On groups with BFC-covered word values
Eloisa Detomi, Marta Morigi, Pavel Shumyatsky
For a group G and a positive integer n write B_n(G) = {x \in G : |x^G | \le n}. If s is a positive integer and w is a group word, say that G satisfies the (n,s)-covering condition…