Geodesic
A commutativity criterion for a group of odd order
Modelirovanie i analiz informacionnyh sistem, Tome 16 (2009) no. 2, pp. 103-108.

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A finite group $G$ is called simply reducible ($SR$-group) if it has the following two properties: 1. Any element of this group is conjugate to its inverse. 2. The tensor product of any two irreducible representations is decomposed into a sum of irreducible representations of the group $G$ with multiplicities at most one. There are some generalizations of $SR$-groups. In particular, a finite group $G$ is called $ASR$-group if the tensor square of any irreducible representation $G$ is decomposed into a sum of irreducible representations of this group with multiplicities at most one. It has been proved that $ASR$-groups of odd order are abelian.
Keywords: finite groups, representations, characters, simply reducible groups. 
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L. S. Kazarin; E. I. Chankov. A commutativity criterion for a group of odd order. Modelirovanie i analiz informacionnyh sistem, Tome 16 (2009) no. 2, pp. 103-108. http://geodesic.mathdoc.fr/item/MAIS_2009_16_2_a5/

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