A group.. is said to have restricted centralizers if for each g epsilon G the centralizer C-G(g) either is finite or has finite index in... Shalev showed that a profinite group with restricted centralizers is virtually abelian. We take interest in profinite groups with restricted centralizers of uniform commutators, that is, elements of the form [x1,.,...xk.], where pi (x1) = pi(x2) = ... =pi (xk). Here, pi(x) denotes the set of prime divisors of the order of...... It is shown that such a group necessarily has an open nilpotent subgroup. We use this result to deduce that gamma k(G) is finite if and only if the cardinality of the set of uniform k-step commutators in G is less than 2(N0).

Detomi E., Morigi M., Shumyatsky P. (2023). Commutators, centralizers, and strong conciseness in profinite groups. MATHEMATISCHE NACHRICHTEN, 296(11), 4948-4960 [10.1002/mana.202200320].

Commutators, centralizers, and strong conciseness in profinite groups

Morigi M.;
2023

Abstract

A group.. is said to have restricted centralizers if for each g epsilon G the centralizer C-G(g) either is finite or has finite index in... Shalev showed that a profinite group with restricted centralizers is virtually abelian. We take interest in profinite groups with restricted centralizers of uniform commutators, that is, elements of the form [x1,.,...xk.], where pi (x1) = pi(x2) = ... =pi (xk). Here, pi(x) denotes the set of prime divisors of the order of...... It is shown that such a group necessarily has an open nilpotent subgroup. We use this result to deduce that gamma k(G) is finite if and only if the cardinality of the set of uniform k-step commutators in G is less than 2(N0).
2023
Detomi E., Morigi M., Shumyatsky P. (2023). Commutators, centralizers, and strong conciseness in profinite groups. MATHEMATISCHE NACHRICHTEN, 296(11), 4948-4960 [10.1002/mana.202200320].
Detomi E.; Morigi M.; Shumyatsky P.
File in questo prodotto:
File Dimensione Formato  
Mathematische Nachrichten - 2023 - Detomi - Commutators centralizers and strong conciseness in profinite groups.pdf

accesso aperto

Tipo: Versione (PDF) editoriale
Licenza: Licenza per Accesso Aperto. Creative Commons Attribuzione (CCBY)
Dimensione 220.77 kB
Formato Adobe PDF
220.77 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/952594
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact