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http://hdl.handle.net/10662/9034
Títulos: | Powers in alternating simple groups |
Autores/as: | Martínez Carracedo, Jorge |
Palabras clave: | Alternating groups;Simple groups;Power subgroups;Word maps;Grupos alternos;Grupos simples;Subgrupos de poder;Mapas de palabras |
Fecha de publicación: | 2015 |
Editor/a: | Universidad de Extremadura |
Resumen: | C. Martínez and E. Zelmanov proved in [12] that for every natural number d and every finite simple group G, there exists a function N = N (d) such that either G d= 1 or G = {a_1^d …a_N^d : a_i ∈ G. In a more general context the problem of finding words ω such that the word map (ɡ1, …, ɡd) → ω (ɡ1, …,ɡd) is surjective for any finite non abelian simple group is a major challenge in Group Theory. In [8] authors give the first example of a word map which is surjective on all finite non-abelian simple groups, the commutator [x; y] (Ore Conjecture). In [11] the conjecture that this is also the case for the word x² y² is formulated. This conjecture was solved in [9] and, independently, in [6], using deep results of algebraic simple groups and representation theory. An elementary proof of this result for alternating simple groups is presented here. |
URI: | http://hdl.handle.net/10662/9034 |
Colección: | Extracta Mathematicae Vol. 30, nº 2 (2015) |
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