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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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | 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| id |
admjournalluguniveduua-article-627 |
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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 |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2018-04-04T09:11:25Z |
| collection |
OJS |
| language |
English |
| topic |
Splittings of groups cohomology of groups commen-surability 20J05 20J06; 20E06 |
| 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 |
| topic_facet |
Splittings of groups cohomology of groups commen-surability 20J05 20J06; 20E06 |
| format |
Article |
| 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 |
| title |
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_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_sort |
note about splittings of groups and commensurability under a cohomological point of view |
| 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/627 |
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