Finite groups with semi-subnormal Schmidt subgroups
A Schmidt group is a non-nilpotent group in which every proper subgroup is nilpotent. A subgroup A of a group G is semi-normal in G if there exists a subgroup B of G such that G = AB and AB1 is a proper subgroup of G for every proper subgroup B1 of B. If A is either subnormal in G or is semi-normal...
Збережено в:
| Видавець: | Інститут прикладної математики і механіки НАН України |
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| Дата: | 2020 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2020
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/188502 |
| Теги: |
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| Цитувати: | Finite groups with semi-subnormal Schmidt subgroups / V.N. Kniahina, V.S. Monakhov // Algebra and Discrete Mathematics. — 2020. — Vol. 29, № 1. — С. 66–73. — Бібліогр.: 17 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | A Schmidt group is a non-nilpotent group in which every proper subgroup is nilpotent. A subgroup A of a group G is semi-normal in G if there exists a subgroup B of G such that G = AB and AB1 is a proper subgroup of G for every proper subgroup B1 of B. If A is either subnormal in G or is semi-normal in G, then A is called a semi-subnormal subgroup of G. In this paper, we establish that a group G with semi-subnormal Schmidt {2, 3}-subgroups is 3-soluble. Moreover, if all 5-closed Schmidt {2, 5}-subgroups are semi-subnormal in G, then G is soluble. We prove that a group with semi-subnormal Schmidt subgroups is metanilpotent. |
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