Author:
CONTRERAS–ROJAS Y.,SHUMYATSKY PAVEL
Abstract
AbstractLet 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.
Publisher
Cambridge University Press (CUP)
Cited by
3 articles.
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