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ON FINITE-BY-NILPOTENT GROUPS

Part of:Structure and classification of infinite or finite groupsSpecial aspects of infinite or finite groups

Published online by Cambridge University Press:  20 December 2019

ELOISA DETOMIOpen the ORCID record for ELOISA DETOMI[Opens in a new window],
GURAM DONADZE,
MARTA MORIGI and
PAVEL SHUMYATSKYOpen the ORCID record for PAVEL SHUMYATSKY[Opens in a new window]
ELOISA DETOMI
Affiliation:
Dipartimento di Ingegneria dell’Informazione - DEI, Università di Padova, Via G. Gradenigo 6/B, 35121 Padova, Italy e-mail: eloisa.detomi@unipd.it
GURAM DONADZE
Affiliation:
Department of Mathematics, University of Brasilia, Brasilia-DF, 70910-900 Brazil and Institute of Cybernetics of the Georgian Technical University, Sandro Euli Str. 5, 0186, Tbilisi, Georgia e-mail: gdonad@gmail.com
MARTA MORIGI
Affiliation:
Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy e-mail: marta.morigi@unibo.it
PAVEL SHUMYATSKY
Affiliation:
Department of Mathematics, University of Brasilia, Brasilia-DF, 70910-900 Brazil e-mail: pavel2040@gmail.com
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Let γn = [x1,…,xn] be the nth lower central word. Denote by Xnthe set of γn -values in a group G and suppose that there is a number m such that $|{g^{{X_n}}}| \le m$ for each g ∈ 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.

MSC classification

Primary:20E45: Conjugacy classes
Secondary:20F12: Commutator calculus20F24: FC-groups and their generalizations

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 63 , Issue 1 , January 2021, pp. 54 - 58
Copyright
© Glasgow Mathematical Journal Trust 2019

Footnotes

The first and third authors are members of INDAM. The fourth author was supported by CNPq-Brazil.

References

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