Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, 2012. / Submitted by Sabrina Silva de Macedo (sabrinamacedo@bce.unb.br) on 2012-07-18T13:02:44Z
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2012_MarinaGabrillaRibeiroBardella.pdf: 1332055 bytes, checksum: bd7481739f43d1c40209e95eb43edade (MD5) / Approved for entry into archive by Patrícia Nunes da Silva(patricia@bce.unb.br) on 2012-09-13T18:31:43Z (GMT) No. of bitstreams: 1
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2012_MarinaGabrillaRibeiroBardella.pdf: 1332055 bytes, checksum: bd7481739f43d1c40209e95eb43edade (MD5) / Um grupo G é um E – grupo (respectivamente, A-grupo) se G é tal que seus elementos comutam com suas respectivas imagens endomorfas (respectivamente, automorfas).Neste trabalho, estudamos algumas propriedades de E-grupos baseadas nos artigos\3-generator groups whose elements commute with their endomorphic images areabelian" e \Minimal number of generators and minimum order of a non-abelian groupwhose elements commute with their endomorphic images", ambos de A. Abdollahi, A.Faghihi e A. Mohammadi Hassanabadi. É possível mostrar que qualquer E-grupo e A-grupo possui classe de nilpotência no máximo 3. Em \Finite 3-groups of class 3 whose elements commute with their automorphic images", A. Abdollahi, A. Faghihi, S. A. Linton, e E. A. O'Brien mostraram que esse máximo _e atingido; para isso construíram um exemplo de um A-grupo de classe de nilpotência exatamente 3. Baseado nesse artigo, estudamos os aspectos teóricos e certos detalhes dos algoritmos (e suas implementações) usados para a construção de tal grupo. ______________________________________________________________________________ ABSTRACT / A group G is an E-group (respectively A-group) if G is such that its elements commute with their endomorphic (respectively automorphic) images. In this work, we study some properties of E-groups based on the papers\3-generatorgroups whose elements commute with their endomorphic images are abelian" and \Minimalnumber of generators and minimum order of a non-abelian group whose elements commute with their endomorphic images", both by A. Abdollahi, A. Faghihi and A.Mohammadi Hassanabadi.It is possible to show that such groups have nilpotency class at most 3. In \Finite3-groups of class 3 whose elements commute with their automorphic images", A. Abdollahi,A. Faghihi, S. A. Linton, and E. A. O'Brien showed that this maximum is reached. To do so they constructed an A-group having nilpotency class precisely 3. Based onthis paper, we study the theoretical aspects and certain details of the algorithms (andtheir implementations) used for the construction of such group.
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.unb.br:10482/11163 |
| Date | 07 March 2012 |
| Creators | Bardella, Marina Gabriella Ribeiro |
| Contributors | Rocco, Noraí Romeu |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/masterThesis |
| Source | reponame:Repositório Institucional da UnB, instname:Universidade de Brasília, instacron:UNB |
| Rights | info:eu-repo/semantics/openAccess |
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