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EnglishThe following two results are proven. (i) Let G be a finitely generated torsion-free linear group. If every torsion-free section of G is an R-group, then G is soluble of finite rank. Conversely, if G has finite rank, then it has a subgroup of finite index, in which every torsion-free section is an R-group. (ii) Let G be a finitely generated torsion-free soluble group. If in every torsion-free section of G the normalizer of each isolated subgroup is isolated, then G has finite rank. Conversely, if G has finite rank, then it has a subgroup K of finite index such that in every torsion-free section of K the normalizer of each isolated subgroup is isolated
| Titolo: | Torsion-free groups with rank restricting properties |
| Autori: | |
| Data di pubblicazione: | 2005 |
| Rivista: | |
| Abstract: | The following two results are proven. (i) Let G be a finitely generated torsion-free linear group. If every torsion-free section of G is an R-group, then G is soluble of finite rank. Conversely, if G has finite rank, then it has a subgroup of finite index, in which every torsion-free section is an R-group. (ii) Let G be a finitely generated torsion-free soluble group. If in every torsion-free section of G the normalizer of each isolated subgroup is isolated, then G has finite rank. Conversely, if G has finite rank, then it has a subgroup K of finite index such that in every torsion-free section of K the normalizer of each isolated subgroup is isolated |
| Handle: | http://hdl.handle.net/11386/1061970 |
| Appare nelle tipologie: | 1.1.2 Articolo su rivista con ISSN |
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