Sets of prime power order generators of finite groups
A subset X of prime power order elements of a finite group G is called pp-independent if there is no proper subset Y of X such that 〈Y,Ф(G)〉 = 〈X,Ф(G)〉, where Ф(G) is the Frattini subgroup of G. A group G has property Bpp if all pp-independent generating sets of G have the same size. G has the pp-ba...
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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/123456789/188508 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Sets of prime power order generators of finite groups / A. Stocka // Algebra and Discrete Mathematics. — 2020. — Vol. 29, № 1. — С. 129–138. — Бібліогр.: 12 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862749394782126080 |
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| author | Stocka, A. |
| author_facet | Stocka, A. |
| citation_txt | Sets of prime power order generators of finite groups / A. Stocka // Algebra and Discrete Mathematics. — 2020. — Vol. 29, № 1. — С. 129–138. — Бібліогр.: 12 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | A subset X of prime power order elements of a finite group G is called pp-independent if there is no proper subset Y of X such that 〈Y,Ф(G)〉 = 〈X,Ф(G)〉, where Ф(G) is the Frattini subgroup of G. A group G has property Bpp if all pp-independent generating sets of G have the same size. G has the pp-basis exchange property if for any pp-independent generating sets B₁,B₂ of G and x ∈ B₁ there exists y ∈ B₂ such that (B₁ \ {x}) ∪ {y} is a pp-independent generating set of G. In this paper we describe all finite solvable groups with property Bpp and all finite solvable groups with the pp-basis exchange property.
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| first_indexed | 2025-12-07T20:59:35Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188508 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T20:59:35Z |
| publishDate | 2020 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Stocka, A. 2023-03-03T16:08:50Z 2023-03-03T16:08:50Z 2020 Sets of prime power order generators of finite groups / A. Stocka // Algebra and Discrete Mathematics. — 2020. — Vol. 29, № 1. — С. 129–138. — Бібліогр.: 12 назв. — англ. 1726-3255 DOI:10.12958/adm1479 2010 MSC: Primary 20D10; Secondary 20F05 https://nasplib.isofts.kiev.ua/handle/123456789/188508 A subset X of prime power order elements of a finite group G is called pp-independent if there is no proper subset Y of X such that 〈Y,Ф(G)〉 = 〈X,Ф(G)〉, where Ф(G) is the Frattini subgroup of G. A group G has property Bpp if all pp-independent generating sets of G have the same size. G has the pp-basis exchange property if for any pp-independent generating sets B₁,B₂ of G and x ∈ B₁ there exists y ∈ B₂ such that (B₁ \ {x}) ∪ {y} is a pp-independent generating set of G. In this paper we describe all finite solvable groups with property Bpp and all finite solvable groups with the pp-basis exchange property. This article has received financial support from the Polish Ministry of Science and Higher Education under subsidy for maintaining the research potential of the Faculty of Mathematics and Informatics, University of Białystok. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Sets of prime power order generators of finite groups Article published earlier |
| spellingShingle | Sets of prime power order generators of finite groups Stocka, A. |
| title | Sets of prime power order generators of finite groups |
| title_full | Sets of prime power order generators of finite groups |
| title_fullStr | Sets of prime power order generators of finite groups |
| title_full_unstemmed | Sets of prime power order generators of finite groups |
| title_short | Sets of prime power order generators of finite groups |
| title_sort | sets of prime power order generators of finite groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188508 |
| work_keys_str_mv | AT stockaa setsofprimepowerordergeneratorsoffinitegroups |