On groups with small Engel depth

Author:

Brandl Rolf

Abstract

Every finite group G satisfies a law [x, ry] = [x, sy] for some positive integers r < s. The minimal value of r is called the depth of G. It is well known that groups of depth 1 are abelian. In this paper we prove the following. Let G be a finite group of depth 2. Then G/F(G) is supersoluble, metabelian and has abelian Sylow p-subgroups for all odd primes p. Moreover, lp(G) ≤ 1 for p odd and l2(G2) ≤ 1.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference12 articles.

Cited by 7 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On the existence of Engel pairs in certain linear groups;Journal of Algebra and Its Applications;2016-02-19

2. On laws of the form $ab\equiv ba$ equivalent to the abelian law;Rendiconti del Seminario Matematico della Università di Padova;2016

3. ON n-ENGEL PAIR SATISFYING CERTAIN CONDITIONS;Journal of Algebra and Its Applications;2014-01-09

4. ON CERTAIN PAIRS OF NON-ENGEL ELEMENTS IN FINITE GROUPS;Journal of Algebra and Its Applications;2013-05-07

5. Generalizations of Brandl's theorem on Engel length;AIP Conference Proceedings;2013

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