Sesión Álgebra, Álgebra Conmutativa, Teoría de GruposFinite groups with high commuting probability for Sylow subgroups
Débora Senise
Universidade de Brasília, Brazil - Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.
Given two subsets \(X,Y\) of a finite group \(G\), we write \(\Pr(X,Y)\) for the probability that random elements \(x \in X\) and \(y \in Y\) commute. If \(X,Y\) are subgroups, we denote by \(\Pr^*(X,Y)\) the maximum real number \(\epsilon\) with the property that for every pair of distinct primes \(p\in\pi(X)\) and \(q\in\pi(Y)\) there is a Sylow \(p\)-subgroup \(P\) of \(X\) and a Sylow \(q\)-subgroup \(Q\) of \(Y\) such that \(\Pr(P,Q) \geq \epsilon\).
In this talk we will discuss finite groups \(G\) with high probabilities \(\Pr^*(T,G)\), where \(T\) is either a term of the lower central series of \(G\) or the generalized Fitting subgroup \(F_i^*(G)\), and show that the structure of such groups is similar, in some precise sense, to that of nilpotent groups.
Trabajo en conjunto con: Eloisa Detomi (Università degli Studi di Padova, Italia) y Pavel Shumyatsky (Universidade de Brasília, Brazil).
Referencias
[1] Eloisa Detomi, Débora Senise, Pavel Shumyatsky, Finite groups with high commuting probability for Sylow subgroups, Journal of Algebra, Volume 711, 2027, Pages 1-13, ISSN 0021-8693, https://doi.org/10.1016/j.jalgebra.2026.06.034.