5 papers · 1 filter
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…
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…
Commuting probability for the Sylow subgroups of a finite group
Eloisa Detomi, Andrea Lucchini, Marta Morigi +1
For subsets of a finite group , let denote the probability that two random elements and commute. Obviously, a finite group is nilpotent if…
Probabilistic properties of profinite groups
Eloisa Detomi, Andrea Lucchini, Marta Morigi +1
Let be a class of finite groups which is closed for subgroups, quotients and direct products. Given a profinite group and an element , we denote by $P_{\m…
Procyclic coverings of commutators in profinite groups
Gustavo A. Fernández-Alcober, Marta Morigi, Pavel Shumyatsky
We consider profinite groups in which all commutators are contained in a union of finitely many procyclic subgroups. It is shown that if G is a profinite group in which all commuta…