УДК 512.542
MSC: 20D10; 20D35
DOI: 10.21538/0134-4889-2021-27-1-268-272
Full text
This paper is based on the results of the 2020 Ural Workshop on Group Theory and Combinatorics
We describe the structure of finite groups with $\mathfrak{F}$-subnormal or self-normalizing primary cyclic subgroups when $\mathfrak{F}$ is a subgroup-closed saturated superradical formation containing all nilpotent groups. We prove that groups with absolutely $\mathfrak{F}$-subnormal or self-normalizing primary cyclic subgroups are soluble when $\mathfrak{F}$ is a subgroup-closed saturated formation containing all nilpotent groups.
Keywords: finite group, primary cyclic subgroup, subnormal subgroup, abnormal subgroup, derived subgroup
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Received October 19, 2020
Revised January 15, 2021
Accepted January 25, 2021
Irina Leonidovna Sokhor, Can. Phys.-Math. Sci., Doc., Brest State A.S.Pushkin University, 224000 Brest, Belarus, e-mail: irina.sokhor@gmail.com
Cite this article as: I.L. Sokhor, Continuation of the theory of $E_\mathfrak{F}$-groups, Trudy Instituta Matematiki i Mekhaniki URO RAN, 2021, vol. 27, no. 1, pp. 268–272.
Русский
И.Л. Сохор. Развитие теории конечных $E_\mathfrak{F}$-групп
Описана структура конечных групп с $\mathfrak{F}$-субнормальными или самонормализуемыми примарными циклическими подгруппами в случае, когда $\mathfrak{F}$ - наследственная насыщенная сверхрадикальная формация, содержащая все нильпотентные группы. Доказано, что группы с абсолютно $\mathfrak{F}$-субнормальными или самонормализуемыми примарными циклическими подгруппамии разрешимы, если $\mathfrak{F}$ - наследственная насыщенная формация, содержащая все нильпотентные группы.
Ключевые слова: конечная группа, примарная циклическая подгруппа, субнормальная подгруппа, абнормальная подгруппа, коммутант
