Geodesic
On finite simply reducible groups
Algebra i analiz, Tome 19 (2007) no. 6, pp. 86-116.

Voir la notice de l'article provenant de la source Math-Net.Ru

A finite $G$ group is said to be simply reducible ($SR$-group) if it has the following two properties: 1) each element of $G$ is conjugate to its inverse; 2) the tensor product of every two irreducible representations is decomposed as a sum of irreducible representations of $G$ with multiplicities not exceeding 1. It is proved that a finite $SR$-group is solvable if it has no composition factors isomorphic to the alternating groups $A_5$ or $A_6$.
Keywords: Group, subgroup, irreducible representation, character, tensor product, real element. 
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L. S. Kazarin; V. V. Yanishevskii. On finite simply reducible groups. Algebra i analiz, Tome 19 (2007) no. 6, pp. 86-116. http://geodesic.mathdoc.fr/item/AA_2007_19_6_a3/

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