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...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2020 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/188502 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862564634946437120 |
|---|---|
| author | Kniahina, V.N. Monakhov, V.S. |
| author_facet | Kniahina, V.N. Monakhov, V.S. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | 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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| first_indexed | 2025-11-25T23:55:40Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-188502 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-25T23:55:40Z |
| publishDate | 2020 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Kniahina, V.N. Monakhov, V.S. 2023-03-03T15:51:45Z 2023-03-03T15:51:45Z 2020 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. 1726-3255 DOI:10.12958/adm1376 2010 MSC: 20E28, 20E32, 20E34 https://nasplib.isofts.kiev.ua/handle/123456789/188502 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Finite groups with semi-subnormal Schmidt subgroups Article published earlier |
| spellingShingle | Finite groups with semi-subnormal Schmidt subgroups Kniahina, V.N. Monakhov, V.S. |
| title | Finite groups with semi-subnormal Schmidt subgroups |
| title_full | Finite groups with semi-subnormal Schmidt subgroups |
| title_fullStr | Finite groups with semi-subnormal Schmidt subgroups |
| title_full_unstemmed | Finite groups with semi-subnormal Schmidt subgroups |
| title_short | Finite groups with semi-subnormal Schmidt subgroups |
| title_sort | finite groups with semi-subnormal schmidt subgroups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188502 |
| work_keys_str_mv | AT kniahinavn finitegroupswithsemisubnormalschmidtsubgroups AT monakhovvs finitegroupswithsemisubnormalschmidtsubgroups |