Lower central words in finite p-groups.

  1. de las Heras, Iker
  2. Morigi, Marta
Publicacions matematiques

ISSN: 0214-1493

Year of publication: 2021

Volume: 65

Issue: 1

Pages: 243-269

Type: Article


More publications in: Publicacions matematiques


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.

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