In the paper, the notion of an \(\mathfrak F^{\omega}\)-abnormal (and \(\mathfrak F^{\omega}\)-normal) maximal subgroup of a finite group is introduced, where \(\mathfrak F\) is a nonempty class of groups and \(\omega\) is a nonempty set of primes. The relationship between the \(\mathfrak F^{\omega}\)- abnormal maximal and normal subgroups is studied. Conditions are established under which \(\mathfrak F^{\omega}\)-abnormal maximal subgroups in a finite group are normal.

中文翻译：

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关于\（\ mathfrak F ^ {\ omega} \）-有限群的异常极大子群的正态性

在本文中，介绍了有限组的\（\ mathfrak F ^ {\ omega} \）-异常（和\（\ mathfrak F ^ {\ omega} \）-normal）最大子组的概念，其中\ （\ mathfrak F \）是一组非空类，而\（\ omega \）是一组非空素数。研究了\（\ mathfrak F ^ {\ omega} \）-异常最大子群与正常子群之间的关系。建立了有限组中\（\ mathfrak F ^ {\ omega} \）-异常最大子组是正常的条件。