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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| Date: | 2018 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/627 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | 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. |
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