A note about splittings of groups and commensurability under a cohomological point of view
Let \(G\) be a group, let \(S\) be a subgroup with infinite index in \(G\) and let \(\mathcal{F}_SG\) be a certain \(\mathbb{Z}_2G\)-module. In this paper, using the cohomological invariant \(E(G, S, \mathcal{F}_SG)\) or simply \(\tilde{E}(G,S)\) (defined in [2]), we analyze some results about split...
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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/627 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543395837640704 |
|---|---|
| author | Andrade, Maria Gorete Carreira Fanti, Ermınia de Lourdes Campelloi |
| author_facet | Andrade, Maria Gorete Carreira Fanti, Ermınia de Lourdes Campelloi |
| author_sort | Andrade, Maria Gorete Carreira |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-04T09:11:25Z |
| description | Let \(G\) be a group, let \(S\) be a subgroup with infinite index in \(G\) and let \(\mathcal{F}_SG\) be a certain \(\mathbb{Z}_2G\)-module. In this paper, using the cohomological invariant \(E(G, S, \mathcal{F}_SG)\) or simply \(\tilde{E}(G,S)\) (defined in [2]), we analyze some results about splittings of group \(G\) over a commensurable with \(S\) subgroup which are related with the algebraic obstruction ``\(\operatorname{sing}_G(S)\)" defined by Kropholler and Roller ([8]. We conclude that \(\tilde{E}(G,S)\) can substitute the obstruction ``\(\operatorname{sing}_G(S)\)" in more general way. We also analyze splittings of groups in the case, when \(G\) and \(S\) satisfy certain duality conditions. |
| first_indexed | 2025-12-02T15:43:01Z |
| format | Article |
| id | admjournalluguniveduua-article-627 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:43:01Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-6272018-04-04T09:11:25Z A note about splittings of groups and commensurability under a cohomological point of view Andrade, Maria Gorete Carreira Fanti, Ermınia de Lourdes Campelloi Splittings of groups, cohomology of groups, commen-surability 20J05, 20J06; 20E06 Let \(G\) be a group, let \(S\) be a subgroup with infinite index in \(G\) and let \(\mathcal{F}_SG\) be a certain \(\mathbb{Z}_2G\)-module. In this paper, using the cohomological invariant \(E(G, S, \mathcal{F}_SG)\) or simply \(\tilde{E}(G,S)\) (defined in [2]), we analyze some results about splittings of group \(G\) over a commensurable with \(S\) subgroup which are related with the algebraic obstruction ``\(\operatorname{sing}_G(S)\)" defined by Kropholler and Roller ([8]. We conclude that \(\tilde{E}(G,S)\) can substitute the obstruction ``\(\operatorname{sing}_G(S)\)" in more general way. We also analyze splittings of groups in the case, when \(G\) and \(S\) satisfy certain duality conditions. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/627 Algebra and Discrete Mathematics; Vol 9, No 2 (2010) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/627/pdf Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | Splittings of groups cohomology of groups commen-surability 20J05 20J06; 20E06 Andrade, Maria Gorete Carreira Fanti, Ermınia de Lourdes Campelloi A note about splittings of groups and commensurability under a cohomological point of view |
| title | A note about splittings of groups and commensurability under a cohomological point of view |
| title_full | A note about splittings of groups and commensurability under a cohomological point of view |
| title_fullStr | A note about splittings of groups and commensurability under a cohomological point of view |
| title_full_unstemmed | A note about splittings of groups and commensurability under a cohomological point of view |
| title_short | A note about splittings of groups and commensurability under a cohomological point of view |
| title_sort | note about splittings of groups and commensurability under a cohomological point of view |
| topic | Splittings of groups cohomology of groups commen-surability 20J05 20J06; 20E06 |
| topic_facet | Splittings of groups cohomology of groups commen-surability 20J05 20J06; 20E06 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/627 |
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