## “On profinite groups with restricted centralizers of $\pi$-elements”

Giovedi 12 Maggio 2022, ore 14:30 - Aula 2AB40 - Cristina Acciarri (Università degli Studi di Modena e Reggio Emilia)

Abstract

A group $G$ is said to have restricted centralizers if for each $g$ in $G$ the centralizer $C_G(g)$ either is finite or has finite index in $G$. This notion was introduced by A. Shalev, who proved that a profinite group in which all centralizers are restricted is virtually abelian, that is, has an abelian subgroup of finite index.

In this talk we will consider a much more general situation, where the restrictedness condition is imposed only on $\pi$-elements of a profinite group $G$, for an arbitrary set of primes $\pi$.