On finite simply reducible groups

Kazarin, L.; Yanishevskiĭ, V.

doi:10.1090/S1061-0022-08-01028-5

On finite simply reducible groups
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by L. S. Kazarin and V. V. Yanishevskiĭ
Translated by: B. M. Bekker

St. Petersburg Math. J. 19 (2008), 931-951

DOI: https://doi.org/10.1090/S1061-0022-08-01028-5

Published electronically: August 21, 2008

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Abstract:

A finite group $G$ 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 $A_6$.

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