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INICIO |
27 de julio de 2024
Active sums I.
| Título inglés | Active sums I. |
|---|---|
| Título español | Sumas activas I. |
| Autor/es | Díaz-Barriga, J. Alejandro ; González-Acuña, Francisco ; Marmolejo, Francisco ; Román, Leopoldo |
| Organización | Inst. Mat. Univ. Nac. Autón. México (UNAM), México D.F., Méjico |
| Revista | 1139-1138 |
| Publicación | 2004, 17 (2): 287-319, 45 Ref. |
| Tipo de documento | articulo |
| Idioma | Inglés |
| Resumen inglés | Given a generating family F of subgroups of a group G closed under conjugation and with partial order compatible with inclusion, a new group S can be constructed, taking into account the multiplication in the subgroups and their mutual actions given by conjugation. The group S is called the active sum of F, has G as a homomorph and is such that S/Z(S) @ G/Z(G) where Z denotes the center. The basic question we investigate in this paper is: when is the active sum S of the family F isomorphic to the group G? The conditions found to answer this question are often of a homological nature. We show that the following groups are active sums of cyclic subgroups: free groups, semidirect products of cyclic groups, Coxeter groups, Wirtinger approximations, groups of order p3 with p an odd prime, simple groups with trivial Schur multiplier, and special linear groups SLn(q) with a few exceptions. We show as well that every finite group G such that G/G' is not cyclic is the active sum of proper normal subgroups. |
| Clasificación UNESCO | 120106 |
| Palabras clave español | Grupos finitos ; Grupos cíclicos ; Subgrupos |
| Código MathReviews | MR2083957 |
| Código Z-Math | Zbl 1069.20046 |
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