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p-nilpotency criteria for some verbal subgroups

2022; Elsevier BV; Volume: 609; Linguagem: Inglês

10.1016/j.jalgebra.2022.07.017

1090-266X

Yerko Contreras-Rojas, Valentina Grazian, Carmine Monetta,

semigroups and automata theory

In this paper we address the problem of understanding when a verbal subgroup of a finite group is p-nilpotent, with p a prime, that is, when all its elements of p′-order determine a subgroup. We provide two p-nilpotency criteria, one for the terms of the lower central series of any finite group and one for the terms of the derived series of any finite soluble group, which relies on arithmetic properties related to the order of products of commutators.