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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Veröffentlicht in:Algebra and Discrete Mathematics
Datum:2020
Hauptverfasser: Fanti, E.L.C., Silva, L.S.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут прикладної математики і механіки НАН України 2020
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/188562
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Zitieren: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.

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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.
first_indexed 2025-12-07T18:45:47Z
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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
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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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