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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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Інститут прикладної математики і механіки НАН України
2020
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/188499 |
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irk-123456789-1884992023-03-04T01:27:00Z A new characterization of finite σ-soluble PσT-groups Adarchenko, N.M. 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. 2020 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/188499 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| 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. |
| format |
Article |
| author |
Adarchenko, N.M. |
| spellingShingle |
Adarchenko, N.M. A new characterization of finite σ-soluble PσT-groups Algebra and Discrete Mathematics |
| author_facet |
Adarchenko, N.M. |
| author_sort |
Adarchenko, N.M. |
| title |
A new characterization of finite σ-soluble PσT-groups |
| title_short |
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_sort |
new characterization of finite σ-soluble pσt-groups |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2020 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/188499 |
| 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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT adarchenkonm anewcharacterizationoffinitessolublepstgroups AT adarchenkonm newcharacterizationoffinitessolublepstgroups |
| first_indexed |
2023-10-18T23:08:30Z |
| last_indexed |
2023-10-18T23:08:30Z |
| _version_ |
1796157354593484800 |