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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| Datum: | 2020 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2020
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| Schriftenreihe: | Algebra and Discrete Mathematics |
| Online Zugang: | http://dspace.nbuv.gov.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| Zusammenfassung: | 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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