Eloisa Detomi

activity

20142024

most citedInvariable generation with elements of coprime prime-power order

2 citations · 2 across the 10 of their papers we have counts for

collaborators

10 papers

math.GR2024

Commuting probability for the Sylow subgroups of a profinite group

Eloisa Detomi, Marta Morigi, Pavel Shumyatsky

Given two subgroups $H, K$ of a compact group $G$ , the probability that a random element of $H$ commutes with a random element of $K$ is denoted by $P r (H, K)$ . We show that if $G$ 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…

math.GR2023

Commuting probability for the Sylow subgroups of a finite group

Eloisa Detomi, Andrea Lucchini, Marta Morigi +1

For subsets $X, Y$ of a finite group $G$ , let $P r (X, Y)$ denote the probability that two random elements $x \in X$ and $y \in Y$ commute. Obviously, a finite group $G$ is nilpotent if…

math.GR2023

Probabilistic properties of profinite groups

Eloisa Detomi, Andrea Lucchini, Marta Morigi +1

Let $C$ be a class of finite groups which is closed for subgroups, quotients and direct products. Given a profinite group $G$ and an element $x \in G$ , we denote by $P_{\m…

math.GR2022

Strongly generating elements in finite and profinite groups

Eloisa Detomi, Andrea Lucchini

Given a finite group $G$ and an element $g \in G$ , we may compare the expected number $e (G)$ of elements needed to generate $G$ and the expected number $e (G, g)$ of elements of $G$ n…