A new characterization of finite σ-soluble PσT-groups
Let σ = {σi | i ∈ I} be a partition of the set of all primes ℙ and G a finite group. G is said to be σ-soluble if every chief factor H/K of G is a σᵢ-group for some i = i(H/K). A set H of subgroups of G is said to be a complete Hall σ-set of G if every member ≠ 1 of H is a Hall σᵢ-subgroup of G for...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2020 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2020
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/188499 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | A new characterization of finite σ-soluble PσT-groups / N.M. Adarchenko // Algebra and Discrete Mathematics. — 2020. — Vol. 29, № 1. — С. 33–41. — Бібліогр.: 18 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862708704179126272 |
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| author | Adarchenko, N.M. |
| author_facet | Adarchenko, N.M. |
| citation_txt | A new characterization of finite σ-soluble PσT-groups / N.M. Adarchenko // Algebra and Discrete Mathematics. — 2020. — Vol. 29, № 1. — С. 33–41. — Бібліогр.: 18 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | Let σ = {σi | i ∈ I} be a partition of the set of all primes ℙ and G a finite group. G is said to be σ-soluble if every chief factor H/K of G is a σᵢ-group for some i = i(H/K). A set H of subgroups of G is said to be a complete Hall σ-set of G if every member ≠ 1 of H is a Hall σᵢ-subgroup of G for some σᵢ∈ σ and H contains exactly one Hall σᵢ-subgroup of G for every i such that σᵢ ∩ π(G) ≠ ∅. A subgroup A of G is said to be σ-quasinormal or σ-permutable in G if G has a complete Hall σ-set H such that AHˣ = HˣA for all x ∈ G and all H ∈ H. We obtain a new characterization of finite σ-soluble groups G in which σ-permutability is a transitive relation in G.
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| first_indexed | 2025-12-07T17:12:18Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-188499 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T17:12:18Z |
| publishDate | 2020 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Adarchenko, N.M. 2023-03-03T15:43:45Z 2023-03-03T15:43:45Z 2020 A new characterization of finite σ-soluble PσT-groups / N.M. Adarchenko // Algebra and Discrete Mathematics. — 2020. — Vol. 29, № 1. — С. 33–41. — Бібліогр.: 18 назв. — англ. 1726-3255 DOI:10.12958/adm1530 2010 MSC: 20D10, 20D15, 20D30 https://nasplib.isofts.kiev.ua/handle/123456789/188499 Let σ = {σi | i ∈ I} be a partition of the set of all primes ℙ and G a finite group. G is said to be σ-soluble if every chief factor H/K of G is a σᵢ-group for some i = i(H/K). A set H of subgroups of G is said to be a complete Hall σ-set of G if every member ≠ 1 of H is a Hall σᵢ-subgroup of G for some σᵢ∈ σ and H contains exactly one Hall σᵢ-subgroup of G for every i such that σᵢ ∩ π(G) ≠ ∅. A subgroup A of G is said to be σ-quasinormal or σ-permutable in G if G has a complete Hall σ-set H such that AHˣ = HˣA for all x ∈ G and all H ∈ H. We obtain a new characterization of finite σ-soluble groups G in which σ-permutability is a transitive relation in G. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics A new characterization of finite σ-soluble PσT-groups Article published earlier |
| spellingShingle | A new characterization of finite σ-soluble PσT-groups Adarchenko, N.M. |
| title | A new characterization of finite σ-soluble PσT-groups |
| title_full | A new characterization of finite σ-soluble PσT-groups |
| title_fullStr | A new characterization of finite σ-soluble PσT-groups |
| title_full_unstemmed | A new characterization of finite σ-soluble PσT-groups |
| title_short | A new characterization of finite σ-soluble PσT-groups |
| title_sort | new characterization of finite σ-soluble pσt-groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188499 |
| work_keys_str_mv | AT adarchenkonm anewcharacterizationoffiniteσsolublepσtgroups AT adarchenkonm newcharacterizationoffiniteσsolublepσtgroups |