Let γn = [x1,... ,xn] be the nth lower central word. Denote by Xn the set of γn -values in a group G and suppose that there is a number m such that for each g a G. We prove that γn+1(G) has finite (m, n) -bounded order. This generalizes the much-celebrated theorem of B. H. Neumann that says that the commutator subgroup of a BFC-group is finite.

Detomi E., Donadze G., Morigi M., Shumyatsky P. (2021). ON FINITE-BY-NILPOTENT GROUPS. GLASGOW MATHEMATICAL JOURNAL, 63(1), 54-58 [10.1017/S0017089519000508].

ON FINITE-BY-NILPOTENT GROUPS

Morigi M.;
2021

Abstract

Let γn = [x1,... ,xn] be the nth lower central word. Denote by Xn the set of γn -values in a group G and suppose that there is a number m such that for each g a G. We prove that γn+1(G) has finite (m, n) -bounded order. This generalizes the much-celebrated theorem of B. H. Neumann that says that the commutator subgroup of a BFC-group is finite.
2021
Detomi E., Donadze G., Morigi M., Shumyatsky P. (2021). ON FINITE-BY-NILPOTENT GROUPS. GLASGOW MATHEMATICAL JOURNAL, 63(1), 54-58 [10.1017/S0017089519000508].
Detomi E.; Donadze G.; Morigi M.; Shumyatsky P.
File in questo prodotto:
File Dimensione Formato  
1907.02798.pdf

accesso aperto

Tipo: Postprint
Licenza: Licenza per Accesso Aperto. Creative Commons Attribuzione - Non commerciale - Non opere derivate (CCBYNCND)
Dimensione 250.88 kB
Formato Adobe PDF
250.88 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/11585/789414
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 6
social impact