Title:	Profinite groups with restricted centralizers of π-elements
Authors:	Acciarri, Cristina Shumyatsky, Pavel
Assunto::	Grupos profinitos π-elementos
Issue Date:	7-Jan-2022
Publisher:	Springer
Citation:	ACCIARRI, Cristina, SHUMYATSKY, Pavel. Profinite groups with restricted centralizers of π-elements. Mathematische Zeitschrift, 2022. DOI: https://doi.org/10.1007/s00209-021-02955-9.
Abstract:	A group G is said to have restricted centralizers if for each g in G the centralizer CG(g) either is finite or has finite index in G. Shalev showed that a profinite group with restricted centralizers is virtually abelian. Given a set of primes π, we take interest in profinite groups with restricted centralizers of π-elements. It is shown that such a profinite group has an open subgroup of the form P×Q, where P is an abelian pro-π subgroup and Q is a pro-π′ subgroup. This significantly strengthens a result from our earlier paper.
DOI:	https://doi.org/10.1007/s00209-021-02955-9
metadata.dc.relation.publisherversion:	https://link.springer.com/article/10.1007%2Fs00209-021-02955-9
Appears in Collections:	Artigos publicados em periódicos e afins

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