Some properties of E(G,W,F_TG) and an application in the theory of splittings of groups
Let us consider \(W\) a \(G\)-set and \(M\) a \(\mathbb{Z}_2G\)-module, where \(G\) is a group. In this paper we investigate some properties of the cohomological the theory of splittings of groups. Namely, we give a proof of the invariant \(E(G,W,M)\), defined in [5] and present related results wit...
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| Datum: | 2021 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2021
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1246 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543290141179904 |
|---|---|
| author | Fanti, E. L. C. Silva, L. S. |
| author_facet | Fanti, E. L. C. Silva, L. S. |
| author_sort | Fanti, E. L. C. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2021-01-29T09:38:49Z |
| description | Let us consider \(W\) a \(G\)-set and \(M\) a \(\mathbb{Z}_2G\)-module, where \(G\) is a group. In this paper we investigate some properties of the cohomological the theory of splittings of groups. Namely, we give a proof of the invariant \(E(G,W,M)\), defined in [5] and present related results with independence of \(E(G,W,M)\) with respect to the set of \(G\)-orbit representatives in \(W\) and properties of the invariant \(E(G,W,\mathcal{F}_TG)\) establishing a relation with the end of pairs of groups \(\widetilde{e}(G,T)\), defined by Kropphller and Holler in [15]. The main results give necessary conditions for \(G\) to split over a subgroup \(T\), in the cases where \(M=\mathbb{Z}_2(G/T)\) or \(M=\mathcal{F}_TG\). |
| first_indexed | 2025-12-02T15:25:15Z |
| format | Article |
| id | admjournalluguniveduua-article-1246 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:25:15Z |
| publishDate | 2021 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-12462021-01-29T09:38:49Z Some properties of E(G,W,F_TG) and an application in the theory of splittings of groups Fanti, E. L. C. Silva, L. S. cohomology of groups, cohomological invariants, splittings and derivation of groups 20E06, 20J06, 57M07 Let us consider \(W\) a \(G\)-set and \(M\) a \(\mathbb{Z}_2G\)-module, where \(G\) is a group. In this paper we investigate some properties of the cohomological the theory of splittings of groups. Namely, we give a proof of the invariant \(E(G,W,M)\), defined in [5] and present related results with independence of \(E(G,W,M)\) with respect to the set of \(G\)-orbit representatives in \(W\) and properties of the invariant \(E(G,W,\mathcal{F}_TG)\) establishing a relation with the end of pairs of groups \(\widetilde{e}(G,T)\), defined by Kropphller and Holler in [15]. The main results give necessary conditions for \(G\) to split over a subgroup \(T\), in the cases where \(M=\mathbb{Z}_2(G/T)\) or \(M=\mathcal{F}_TG\). Lugansk National Taras Shevchenko University FAPESP CAPES 2021-01-29 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1246 10.12958/adm1246 Algebra and Discrete Mathematics; Vol 30, No 2 (2020) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1246/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1246/429 Copyright (c) 2021 Algebra and Discrete Mathematics |
| spellingShingle | cohomology of groups cohomological invariants splittings and derivation of groups 20E06 20J06 57M07 Fanti, E. L. C. Silva, L. S. Some properties of E(G,W,F_TG) and an application in the theory of splittings of groups |
| title | Some properties of E(G,W,F_TG) and an application in the theory of splittings of groups |
| title_full | Some properties of E(G,W,F_TG) and an application in the theory of splittings of groups |
| title_fullStr | Some properties of E(G,W,F_TG) and an application in the theory of splittings of groups |
| title_full_unstemmed | Some properties of E(G,W,F_TG) and an application in the theory of splittings of groups |
| title_short | Some properties of E(G,W,F_TG) and an application in the theory of splittings of groups |
| title_sort | some properties of e(g,w,f_tg) and an application in the theory of splittings of groups |
| topic | cohomology of groups cohomological invariants splittings and derivation of groups 20E06 20J06 57M07 |
| topic_facet | cohomology of groups cohomological invariants splittings and derivation of groups 20E06 20J06 57M07 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1246 |
| work_keys_str_mv | AT fantielc somepropertiesofegwftgandanapplicationinthetheoryofsplittingsofgroups AT silvals somepropertiesofegwftgandanapplicationinthetheoryofsplittingsofgroups |