Thin systems of generators of groups
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Thin systems of generators of groups
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| Creator |
Lutsenko, I.
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| Description |
A subset T of a group G with the identity e is called k-thin (k∈N) if |A∩gA| ≤ k, |A∩Ag| ≤ k for every g∈G, g≠e. We show that every infinite group G can be generated by some 2-thin subset. Moreover, if G is either Abelian or a torsion group without elements of order 2, then there exists a 1-thin system of generators of G. For every infinite group G, there exist a 2-thin subset X such that G=XX⁻¹ ∪ X⁻¹X, and a 4-thin subset Y such that G=YY⁻¹.
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| Date |
2019-06-15T16:21:07Z
2019-06-15T16:21:07Z 2010 |
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| Type |
Article
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| Identifier |
Thin systems of generators of groups / I. Lutsenko // Algebra and Discrete Mathematics. — 2010. — Vol. 9, № 2. — С. 106–112. — Бібліогр.: 6 назв. — англ.
1726-3255 2000 Mathematics Subject Classification:20F05, 20F99. http://dspace.nbuv.gov.ua/handle/123456789/154507 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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