On some classes of finite σ-soluble PσT-groups

I. N. Safonova, A. Skiba
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Abstract

Let X be a class of groups. Suppose that with each group G ∈ X we associate some system of its subgroups τ(G). Then τ is said to be a subgroup functor on X if the following conditions are hold: (1) G ∈  τ(G) for each group G ∈ X; (2) for any epimorphism φ: A → B, where A, B ∈ X, and for any groups H ∈ τ(A) and T ∈ τ(B) we have Hφ ∈ τ(B) and Tφ-1 ∈ τ( A). In this paper, were considered some applications of such subgroup functors in the theory of finite groups in which generalized normality for subgroups is transitive.
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关于有限σ可溶PσT群的一些类别
让 X 是一类群。假设每个群 G∈X 都与它的子群 τ(G) 关联。那么,如果以下条件成立,我们就说 τ 是 X 上的一个子群函子:(1)对于每个群 G∈X,G∈τ(G);(2)对于任何外形变 φ:A→B,其中 A,B∈X,对于任何群 H∈τ(A) 和 T∈τ(B) 我们有 Hφ∈τ(B) 和 Tφ-1∈τ( A)。本文考虑了这种子群函数在有限群理论中的一些应用,在有限群理论中,子群的广义正则性是反式的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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