Article contents
Nonsoluble length of finite groups with commutators of small order
Published online by Cambridge University Press: 13 February 2015
Abstract
Let p be a prime. Every finite group G has a normal series each of whose quotients either is p-soluble or is a direct product of nonabelian simple groups of orders divisible by p. The non-p-soluble length λp(G) is defined as the minimal number of non-p-soluble quotients in a series of this kind.
We deal with the question whether, for a given prime p and a given proper group variety , there is a bound for the non-p-soluble length λp of finite groups whose Sylow p-subgroups belong to . Let the word w be a multilinear commutator. In this paper we answer the question in the affirmative in the case where p is odd and the variety is the one of groups satisfying the law we ≡ 1.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 158 , Issue 3 , May 2015 , pp. 487 - 492
- Copyright
- Copyright © Cambridge Philosophical Society 2015
References
REFERENCES
- 3
- Cited by