Lower central words in finite p-groups.

• Autores: Iker de las Heras Kerejeta, Marta Morigi
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 65, Nº 1, 2021, págs. 243-269
• Idioma: inglés
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• Resumen

  • 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.