Abstract Let 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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关于σ-可溶群的一个开放问题

Abstract 令是所有素数集合的某个划分，即对于所有令 G 是一个有限群。如果 G 的每个非同一成员都是 G 的霍尔 σi-子群，并且对于每个 G 恰好包含一个霍尔 σi-子群，则称 G 的一组子群是 G 的完整霍尔 σ-集。 -group 如果它拥有完整的霍尔 σ 集。σ-群 G 被认为是 σ-色散的，前提是 G 有一个正规级数和一个完整的霍尔 σ-集，使得对于所有在这篇文章中，我们给出了一个 σ-色散群的表征，它给出了一个正答案Skiba的开放问题。