On an open problem of σ-soluble groups

摘要

AbstractLet be some partition of the set of all primes, that is, and for all Let G be a finite group. A set of subgroups of G is said to be a complete Hall σ-set of G if every nonidentity member of is a Hall σi-subgroup of G and contains exactly one Hall σi-subgroup of G for every G is said to be a σ-group if it possesses a complete Hall σ-set. A σ-group G is said to be σ-dispersive provided G has a normal series and a complete Hall σ-set such that for all In this article, we give a characterization of σ-dispersive group, which gives a positive answer to an open problem of Skiba.

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