Some properties of nilpotent groups
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Some properties of nilpotent groups
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| Creator |
Gaglione, A.M.
Lipschutz, S. Spellman, D. |
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| 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.
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| Date |
2019-06-15T16:41:10Z
2019-06-15T16:41:10Z 2009 |
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| Type |
Article
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| Identifier |
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 |
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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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