The cohomological invariant E'(G,W) and some properties

Detalhes bibliográficos
Autor(a) principal: Andrade, Maria Gorete Carreira [UNESP]
Data de Publicação: 2012
Outros Autores: Fanti, Ermínia de Lourdes Campello [UNESP]
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]).
id UNSP_314c4b1d402d12fe551d048f27f7a77e
oai_identifier_str oai:repositorio.unesp.br:11449/122693
network_acronym_str UNSP
network_name_str Repositório Institucional da UNESP
repository_id_str 2946
spelling 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