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.
Contreras-Rojas, Y., Grazian, V., Monetta, C. (2022). p-nilpotency criteria for some verbal subgroups. JOURNAL OF ALGEBRA, 609(1 November 2022), 926-936 [10.1016/j.jalgebra.2022.07.017].
p-nilpotency criteria for some verbal subgroups
Grazian, Valentina
;
2022
Abstract
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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
