Geodesic
Finite simply reducible groups are soluble
Sbornik. Mathematics, Tome 201 (2010) no. 5, pp. 655-668 Cet article a éte moissonné depuis la source Math-Net.Ru

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A finite group $G$ is called simply reducible (briefly, an $SR$-group) if it has the following two properties: every element of this group is conjugate to its inverse; the tensor product of any two irreducible representations decomposes into a sum of irreducible representations of the group $G$ with multiplicities not exceeding 1. It is proved that finite $SR$-groups are soluble. Bibliography: 13 titles.
Keywords: finite groups, characters, multiplicity-free representations, simply reducible groups. 
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L. S. Kazarin; E. I. Chankov. Finite simply reducible groups are soluble. Sbornik. Mathematics, Tome 201 (2010) no. 5, pp. 655-668. http://geodesic.mathdoc.fr/item/SM_2010_201_5_a2/

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