The cohomological invariant E'(G,W) and some properties
Autor(a) principal: | |
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Data de Publicação: | 2012 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://www.diogenes.bg/ijam/contents/index.html http://hdl.handle.net/11449/122693 |
Resumo: | Let G be a group, W a nonempty G-set and M a Z2G-module. Consider the restriction map resG W : H1(G,M) → Pi wi∈E H1(Gwi,M), [f] → (resGG wi [f])i∈I , where E = {wi, i ∈ I} is a set of orbit representatives in W and Gwi = {g ∈ G | gwi = wi} is the G-stabilizer subgroup (or isotropy subgroup) of wi, for each wi ∈ E. In this work we analyze some results presented in Andrade et al [5] about splittings and duality of groups, using the point of view of Dicks and Dunwoody [10] and the invariant E'(G,W) := 1+dimkerresG W, defined when Gwi is a subgroup of infinite index in G for all wi in E, andM = Z2 (where dim = dimZ2). We observe that the theory of splittings of groups (amalgamated free product and HNN-groups) is inserted in the combinatory theory of groups which has many applications in graph theory (see, for example, Serre [12] and Dicks and Dunwoody [10]). |
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The cohomological invariant E'(G,W) and some propertiescohomology of groupsdualitysplittings of groupsLet G be a group, W a nonempty G-set and M a Z2G-module. Consider the restriction map resG W : H1(G,M) → Pi wi∈E H1(Gwi,M), [f] → (resGG wi [f])i∈I , where E = {wi, i ∈ I} is a set of orbit representatives in W and Gwi = {g ∈ G | gwi = wi} is the G-stabilizer subgroup (or isotropy subgroup) of wi, for each wi ∈ E. In this work we analyze some results presented in Andrade et al [5] about splittings and duality of groups, using the point of view of Dicks and Dunwoody [10] and the invariant E'(G,W) := 1+dimkerresG W, defined when Gwi is a subgroup of infinite index in G for all wi in E, andM = Z2 (where dim = dimZ2). We observe that the theory of splittings of groups (amalgamated free product and HNN-groups) is inserted in the combinatory theory of groups which has many applications in graph theory (see, for example, Serre [12] and Dicks and Dunwoody [10]).Universidade Estadual Paulista Júlio de Mesquita Filho, Departamento de Matemática, Instituto de Biociências Letras e Ciências Exatas de São José do Rio Preto, Sao Jose do Rio Preto, Rua Cristóvão Colombo, 2265, Jardim Nazareth, CEP 15054-000, SP, BrasilUniversidade Estadual Paulista Júlio de Mesquita Filho, Departamento de Matemática, Instituto de Biociências Letras e Ciências Exatas de São José do Rio Preto, Sao Jose do Rio Preto, Rua Cristóvão Colombo, 2265, Jardim Nazareth, CEP 15054-000, SP, BrasilUniversidade Estadual Paulista (Unesp)Andrade, Maria Gorete Carreira [UNESP]Fanti, Ermínia de Lourdes Campello [UNESP]2015-04-27T11:55:58Z2015-04-27T11:55:58Z2012info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article183-190http://www.diogenes.bg/ijam/contents/index.htmlInternational Journal of Applied Mathematics, v. 25, n. 2, p. 183-190, 2012.1311-1728http://hdl.handle.net/11449/12269331863375029573660358661907070998Currículo Lattesreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengInternational Journal of Applied Mathematicsinfo:eu-repo/semantics/openAccess2021-10-22T17:27:41Zoai:repositorio.unesp.br:11449/122693Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T17:06:30.586991Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
The cohomological invariant E'(G,W) and some properties |
title |
The cohomological invariant E'(G,W) and some properties |
spellingShingle |
The cohomological invariant E'(G,W) and some properties Andrade, Maria Gorete Carreira [UNESP] cohomology of groups duality splittings of groups |
title_short |
The cohomological invariant E'(G,W) and some properties |
title_full |
The cohomological invariant E'(G,W) and some properties |
title_fullStr |
The cohomological invariant E'(G,W) and some properties |
title_full_unstemmed |
The cohomological invariant E'(G,W) and some properties |
title_sort |
The cohomological invariant E'(G,W) and some properties |
author |
Andrade, Maria Gorete Carreira [UNESP] |
author_facet |
Andrade, Maria Gorete Carreira [UNESP] Fanti, Ermínia de Lourdes Campello [UNESP] |
author_role |
author |
author2 |
Fanti, Ermínia de Lourdes Campello [UNESP] |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Andrade, Maria Gorete Carreira [UNESP] Fanti, Ermínia de Lourdes Campello [UNESP] |
dc.subject.por.fl_str_mv |
cohomology of groups duality splittings of groups |
topic |
cohomology of groups duality splittings of groups |
description |
Let G be a group, W a nonempty G-set and M a Z2G-module. Consider the restriction map resG W : H1(G,M) → Pi wi∈E H1(Gwi,M), [f] → (resGG wi [f])i∈I , where E = {wi, i ∈ I} is a set of orbit representatives in W and Gwi = {g ∈ G | gwi = wi} is the G-stabilizer subgroup (or isotropy subgroup) of wi, for each wi ∈ E. In this work we analyze some results presented in Andrade et al [5] about splittings and duality of groups, using the point of view of Dicks and Dunwoody [10] and the invariant E'(G,W) := 1+dimkerresG W, defined when Gwi is a subgroup of infinite index in G for all wi in E, andM = Z2 (where dim = dimZ2). We observe that the theory of splittings of groups (amalgamated free product and HNN-groups) is inserted in the combinatory theory of groups which has many applications in graph theory (see, for example, Serre [12] and Dicks and Dunwoody [10]). |
publishDate |
2012 |
dc.date.none.fl_str_mv |
2012 2015-04-27T11:55:58Z 2015-04-27T11:55:58Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://www.diogenes.bg/ijam/contents/index.html International Journal of Applied Mathematics, v. 25, n. 2, p. 183-190, 2012. 1311-1728 http://hdl.handle.net/11449/122693 3186337502957366 0358661907070998 |
url |
http://www.diogenes.bg/ijam/contents/index.html http://hdl.handle.net/11449/122693 |
identifier_str_mv |
International Journal of Applied Mathematics, v. 25, n. 2, p. 183-190, 2012. 1311-1728 3186337502957366 0358661907070998 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
International Journal of Applied Mathematics |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
183-190 |
dc.source.none.fl_str_mv |
Currículo Lattes reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808128756480475136 |