Algebra seminar: talk by Cristina Acciarri

On Wednesday 29th March 2023, the Charlotte Centre for Algebra had the pleasure of virtually welcoming Cristina Acciarri (University of Modena and Reggio Emilia & University of Brasilia) for a talk entitled On profinite groups with restricted centralizers of π-elements at the research seminar of Lincoln University.

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 π-elements of a profinite group G, for an arbitrary set of primes π.