Let G be a finite group. The nonsoluble length λ(G) of G is the number of nonsoluble factors in a shortest normal series of G, each of whose factors either is soluble or is a direct product of nonabelian simple groups. In the present paper we are concerned with bounding λ(G) in terms of coprime commutators, that is, commutators [a, b] with (|a|, |b|) = 1. Let e be a positive integer and 2^f the maximal 2-power dividing e. We show that if x^e = 1 whenever x is a coprime commutator in G, then λ(G) ≤ f.

Coprime commutators and the nonsoluble length of a finite group

Maria Tota
In corso di stampa

Abstract

Let G be a finite group. The nonsoluble length λ(G) of G is the number of nonsoluble factors in a shortest normal series of G, each of whose factors either is soluble or is a direct product of nonabelian simple groups. In the present paper we are concerned with bounding λ(G) in terms of coprime commutators, that is, commutators [a, b] with (|a|, |b|) = 1. Let e be a positive integer and 2^f the maximal 2-power dividing e. We show that if x^e = 1 whenever x is a coprime commutator in G, then λ(G) ≤ f.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4810074
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