Some properties of E(G,W,FTG) and an application in the theory of splittings of groups
Let us consider W a G-set and M a Z₂G-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 res...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2020 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/188562 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Some properties of E(G,W,FTG) and an application in the theory of splittings of groups / E.L.C. Fanti, L.S. Silva // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 2. — С. 179–193. — Бібліогр.: 19 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862724152412078080 |
|---|---|
| author | Fanti, E.L.C. Silva, L.S. |
| author_facet | Fanti, E.L.C. Silva, L.S. |
| citation_txt | Some properties of E(G,W,FTG) and an application in the theory of splittings of groups / E.L.C. Fanti, L.S. Silva // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 2. — С. 179–193. — Бібліогр.: 19 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | Let us consider W a G-set and M a Z₂G-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,FTG) establishing a relation with the end of pairs of groups ê(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 = Z₂(G/T ) or M = FTG.
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| first_indexed | 2025-12-07T18:45:47Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188562 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T18:45:47Z |
| publishDate | 2020 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Fanti, E.L.C. Silva, L.S. 2023-03-06T14:31:02Z 2023-03-06T14:31:02Z 2020 Some properties of E(G,W,FTG) and an application in the theory of splittings of groups / E.L.C. Fanti, L.S. Silva // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 2. — С. 179–193. — Бібліогр.: 19 назв. — англ. 1726-3255 DOI:10.12958/adm1246 2010 MSC: 20E06, 20J06, 57M07 https://nasplib.isofts.kiev.ua/handle/123456789/188562 Let us consider W a G-set and M a Z₂G-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,FTG) establishing a relation with the end of pairs of groups ê(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 = Z₂(G/T ) or M = FTG. The authors’ research was supported by FAPESP (grant 12/24454-8, 16/24707-4) and CAPES. We would like to thank to Professor G. P. Scott for the prompt attention and a suggestion for an example. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Some properties of E(G,W,FTG) and an application in the theory of splittings of groups Article published earlier |
| spellingShingle | Some properties of E(G,W,FTG) and an application in the theory of splittings of groups Fanti, E.L.C. Silva, L.S. |
| title | Some properties of E(G,W,FTG) and an application in the theory of splittings of groups |
| title_full | Some properties of E(G,W,FTG) and an application in the theory of splittings of groups |
| title_fullStr | Some properties of E(G,W,FTG) and an application in the theory of splittings of groups |
| title_full_unstemmed | Some properties of E(G,W,FTG) and an application in the theory of splittings of groups |
| title_short | Some properties of E(G,W,FTG) and an application in the theory of splittings of groups |
| title_sort | some properties of e(g,w,ftg) and an application in the theory of splittings of groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188562 |
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