Thin systems of generators of groups
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 sys...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2010 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2010
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/154507 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Thin systems of generators of groups / I. Lutsenko // Algebra and Discrete Mathematics. — 2010. — Vol. 9, № 2. — С. 106–112. — Бібліогр.: 6 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862730565250187264 |
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| author | Lutsenko, I. |
| author_facet | Lutsenko, I. |
| citation_txt | Thin systems of generators of groups / I. Lutsenko // Algebra and Discrete Mathematics. — 2010. — Vol. 9, № 2. — С. 106–112. — Бібліогр.: 6 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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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| first_indexed | 2025-12-07T19:21:21Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154507 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T19:21:21Z |
| publishDate | 2010 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Lutsenko, I. 2019-06-15T16:21:07Z 2019-06-15T16:21:07Z 2010 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. https://nasplib.isofts.kiev.ua/handle/123456789/154507 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Thin systems of generators of groups Article published earlier |
| spellingShingle | Thin systems of generators of groups Lutsenko, I. |
| title | Thin systems of generators of groups |
| title_full | Thin systems of generators of groups |
| title_fullStr | Thin systems of generators of groups |
| title_full_unstemmed | Thin systems of generators of groups |
| title_short | Thin systems of generators of groups |
| title_sort | thin systems of generators of groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154507 |
| work_keys_str_mv | AT lutsenkoi thinsystemsofgeneratorsofgroups |