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On the Normality of $\mathfrak F^{\omega}$-Abnormal Maximal Subgroups of Finite Groups
M. M. Sorokina, S. P. Maksakov I. G. Petrovsky Bryansk State University
Abstract:
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.
Keywords:
finite group,
$\mathfrak F^{\omega}$-abnormal maximal subgroup, normal subgroup,
class of groups, formation.
Received: 23.07.2019 Revised: 23.01.2020
Citation:
M. M. Sorokina, S. P. Maksakov, “On the Normality of $\mathfrak F^{\omega}$-Abnormal Maximal Subgroups of Finite Groups”, Mat. Zametki, 108:3 (2020), 428–440; Math. Notes, 108:3 (2020), 409–418
Linking options:
https://www.mathnet.ru/eng/mzm12521https://doi.org/10.4213/mzm12521 https://www.mathnet.ru/eng/mzm/v108/i3/p428
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