p-nilpotency criteria for some verbal subgroups

被引：2

作者：

Contreras-Rojas, Yerko ^{[1
]}

Grazian, Valentina ^{[2
]}

Monetta, Carmine ^{[3
]}

机构：

[1] Univ Fed Sul & Sudeste Para, Fac Math, Inst Exact Sci, Ave Ipes,Cidade Univ, Maraba, Para, Brazil

[2] Univ Milano Bicocca, Dept Math & Applicat, Via Roberto Cozzi 55, I-20125 Milan, Italy

[3] Univ Salerno, Dept Math, via Giovanni Paolo II 132, I-84084 Fisciano, SA, Italy

来源：

JOURNAL OF ALGEBRA | 2022年 / 609卷

关键词：

p-nilpotency; Lower central word; Derived word; FINITE; COMMUTATORS; ORDERS;

D O I：

10.1016/j.jalgebra.2022.07.017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.(c) 2022 Elsevier Inc. All rights reserved.

引用

页码：926 / 936

页数：11

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