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INICIO | 20 de abril 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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Equipo DML-E
Instituto de Ciencias Matemáticas (ICMAT - CSIC)
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