Lower central words in finite p-groups
de las Heras, Iker (Euskal Herriko Unibertsitatea (UPV/EHU). Zientzia eta Teknologia Fakultatea, Matematika Saila)
Morigi, Marta (Universit'a di Bologna (Bolonia, Italia). Dipartimento di Matematica)

Date:	2021
Abstract:	It is well known that the set of values of a lower central word in a group G need not be a subgroup. For a fixed lower central word γr and for p ≥ 5, Guralnick showed that if G is a finite p-group such that the verbal subgroup γr(G) is abelian and 2-generator, then γr(G) consists only of γr-values. In this paper we extend this result, showing that the assumption that γr(G) is abelian can be dropped. Moreover, we show that the result remains true even if p= 3. Finally, we prove that the analogous result for pro-p groups is true.
Note:	The first author is supported by the Spanish Government, grant MTM2017-86802-P, partly with FEDER funds, and by the Basque Government, grant IT974-16. He is also supported by a predoctoral grant of the University of the Basque Country. The second author is a member of INDAM.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	P-groups ; Commutators ; Lower central words
Published in:	Publicacions matemàtiques, Vol. 65 Núm. 1 (2021) , p. 243-269 (Articles) , ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/383697
DOI: 10.5565/PUBLMAT6512107
DOI: 10.5565/publicacionsmatematiques.v65i1.383697

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