Geodesic
On tensor squares of reducible representations of almost simple groups.~II
Modelirovanie i analiz informacionnyh sistem, Tome 18 (2011) no. 2, pp. 5-17

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Almost simple $\mathrm{SM}_m$-groups are considered. A group $G$ is called $\mathrm{SM}_m$-group if the tensor square of any irreducible representation is decomposed into the sum of all characters with multiplicities not greater than $m$. It turned out that if $G$ is an almost simple $\mathrm{SM}_t$-group, then $G\cong PGL_2(q)$.
Keywords: SR-groups, SM$_m$-groups almost simple groups automorphisms GAP. 
@article{MAIS_2011_18_2_a0,
     author = {S. V. Polyakov},
     title = {On tensor squares of reducible representations of almost simple {groups.~II}},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {5--17},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2011_18_2_a0/}
}
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S. V. Polyakov. On tensor squares of reducible representations of almost simple groups.~II. Modelirovanie i analiz informacionnyh sistem, Tome 18 (2011) no. 2, pp. 5-17. http://geodesic.mathdoc.fr/item/MAIS_2011_18_2_a0/