The main result of this paper states that if \({\mathcal {F}}\) is a subgroup-closed saturated formation of full characteristic, then the \({\mathcal {F}}\)-residual of a K-\({\mathcal {F}}\)-subnormal subgroup S of a finite group G is a large subgroup of G provided that the \({\mathcal {F}}\)-hypercentre of every subgroup X of G containing S is contained in the \({\mathcal {F}}\)-residual of X. This extends a recent result of Aivazidis, Safonova and Skiba.

中文翻译：

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关于 Aivazidis、Safonova 和 Skiba 论文的注释

本文的主要结果表明，如果\({\mathcal {F}}\)是一个全特征的子群闭饱和形成，那么\({\mathcal {F}}\) -残差 K- \（{\ mathcal {F}} \） -subnormal亚组小号有限群G ^是大子组G ^条件是\（{\ mathcal {F}} \）每子组的-hypercentre X的ģ含有小号包含在X的\({\mathcal {F}}\) -残差中。这扩展了 Aivazidis、Safonova 和 Skiba 最近的结果。