O quadrado tensorial não-abeliano, construções relacionadas e p-grupos
Let G and Gφ be two isomorphic groups. We study the group ν(G) that is an extension of the non-abelian tensor square of G, G⊗G. We show how ν(G) preserves properties from the group G in question. We also study potent and powerful finite p-groups. We prove that the non-abelian tensor square of G and...
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| Tipo de recurso: | tesis de maestría |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | Brasil |
| Institución: | Universidade Federal de Goiás (UFG) |
| Repositorio: | Repositório Institucional da UFG |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.bc.ufg.br:tede/13502 |
| Acceso en línea: | http://repositorio.bc.ufg.br/tede/handle/tede/13502 |
| Access Level: | acceso abierto |
| Palabra clave: | Quadrado tensorial não-abeliano de grupos Comutadores Nilpotência Solubilidade P-grupos finitos P-grupos potent e powerful Non-abelian tensor square of groups Cmmutatores Nilpotency Solubility Finite p-groups Potent and powerful p-groups CIENCIAS EXATAS E DA TERRA::MATEMATICA |
| Sumario: | Let G and Gφ be two isomorphic groups. We study the group ν(G) that is an extension of the non-abelian tensor square of G, G⊗G. We show how ν(G) preserves properties from the group G in question. We also study potent and powerful finite p-groups. We prove that the non-abelian tensor square of G and the k-th term of the lower central series of ν(G) are potently embedded in ν(G), when G is a potent finite p-group. Moreover, for an odd prime p, if G is a potent p-group, then exp(ν(G)) divides p · exp(G) |
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