Some properties of nilpotent groups
Property S, a finiteness property which can hold in infinite groups, was introduced by Stallings and others and shown to hold in free groups. In [2] it was shown to hold in nilpotent groups as a consequence of a technical result of Mal'cev. In that paper this technical result was dubbed propert...
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| Дата: | 2009 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут прикладної математики і механіки НАН України
2009
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/154599 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Some properties of nilpotent groups / A.M. Gaglione, S. Lipschutz, D. Spellman // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 4. — С. 66–77. — Бібліогр.: 8 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1545992019-06-16T01:26:29Z Some properties of nilpotent groups Gaglione, A.M. Lipschutz, S. Spellman, D. Property S, a finiteness property which can hold in infinite groups, was introduced by Stallings and others and shown to hold in free groups. In [2] it was shown to hold in nilpotent groups as a consequence of a technical result of Mal'cev. In that paper this technical result was dubbed property R. Hence, more generally, any property R group satisfies property S. In [7] it was shown that property R implies the following (labeled there weak property R) for a group G: If G₀ is any subgroup in G and G₀* is any homomorphic image of G₀, then the set of torsion elements in G₀* forms a locally finite subgroup. It was left as an open question in [7] whether weak property R is equivalent to property R. In this paper we give an explicit counterexample thereby proving that weak property R is strictly weaker than property R. 2009 Article Some properties of nilpotent groups / A.M. Gaglione, S. Lipschutz, D. Spellman // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 4. — С. 66–77. — Бібліогр.: 8 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:20F18,20F05,20F24,16D10. http://dspace.nbuv.gov.ua/handle/123456789/154599 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Property S, a finiteness property which can hold in infinite groups, was introduced by Stallings and others and shown to hold in free groups. In [2] it was shown to hold in nilpotent groups as a consequence of a technical result of Mal'cev. In that paper this technical result was dubbed property R. Hence, more generally, any property R group satisfies property S. In [7] it was shown that property R implies the following (labeled there weak property R) for a group G: If G₀ is any subgroup in G and G₀* is any homomorphic image of G₀, then the set of torsion elements in G₀* forms a locally finite subgroup. It was left as an open question in [7] whether weak property R is equivalent to property R. In this paper we give an explicit counterexample thereby proving that weak property R is strictly weaker than property R. |
| format |
Article |
| author |
Gaglione, A.M. Lipschutz, S. Spellman, D. |
| spellingShingle |
Gaglione, A.M. Lipschutz, S. Spellman, D. Some properties of nilpotent groups Algebra and Discrete Mathematics |
| author_facet |
Gaglione, A.M. Lipschutz, S. Spellman, D. |
| author_sort |
Gaglione, A.M. |
| title |
Some properties of nilpotent groups |
| title_short |
Some properties of nilpotent groups |
| title_full |
Some properties of nilpotent groups |
| title_fullStr |
Some properties of nilpotent groups |
| title_full_unstemmed |
Some properties of nilpotent groups |
| title_sort |
some properties of nilpotent groups |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/154599 |
| citation_txt |
Some properties of nilpotent groups / A.M. Gaglione, S. Lipschutz, D. Spellman // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 4. — С. 66–77. — Бібліогр.: 8 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
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