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.

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

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/}
}
TY  - JOUR
AU  - S. V. Polyakov
TI  - On tensor squares of reducible representations of almost simple groups.~II
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2011
SP  - 5
EP  - 17
VL  - 18
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MAIS_2011_18_2_a0/
LA  - ru
ID  - MAIS_2011_18_2_a0
ER  - 
%0 Journal Article
%A S. V. Polyakov
%T On tensor squares of reducible representations of almost simple groups.~II
%J Modelirovanie i analiz informacionnyh sistem
%D 2011
%P 5-17
%V 18
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MAIS_2011_18_2_a0/
%G ru
%F MAIS_2011_18_2_a0
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/

[1] D. Gorenstein, Finite groups, Harper and Row, N.Y., 1968 | MR | Zbl

[2] P. X. Gallagher, “The number of conjugacy classes in a finite group”, Math. Z., 118 (1970), 175–179 | DOI | MR | Zbl

[3] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, R. A. Wilson, Atlas of Finite, Clarendon Press, Groups. Oxford, 1985 http://brauer.maths.qmul.ac.uk/Atlas/v3/ | MR | Zbl

[4] L. S. Kazarin , V. V. Yanishevskii, “O konechnykh prosto privodimykh gruppakh”, Algebra i analiz, 19:6 (2007), 86–116 | MR

[5] L. S. Kazarin, E. I. Chankov, “Konechnye prosto privodimye gruppy razreshimy”, Matematicheskii sbornik, 201:5 (2010), 27–40 | MR

[6] L. S. Kazarin, I. A. Sagirov, “On the degrees of irreducible characters of finite simple groups”, Proc. of the Steklov Inst. Math., 2001, Suppl., no. 2, 71–81 | MR

[7] I. M. Isaacs, Character theory of finite groups, Acad. Press, N.Y., 1976 | MR | Zbl

[8] W. A. Simpson, W. A. Frame, “The character tables for $SL(3,q)$, $SU(3,q)$, $PSL(3,q)$, $PSU(3,q)$”, Can. J. Math., XXV:3 (1973), 486–494 | DOI | MR | Zbl

[9] A. Maróti, “Bounding the number of conjugacy classes of a permutation group”, Journal of Group Theory, 8:3 (2005), 273–289 | DOI | MR | Zbl

[10] The GAP Group, GAP — Groups, Algorithms and Programming, Version 4.4.10, , St. Andrews, Aachen, 2008 http://www.gap-system.org

[11] S. V. Polyakov, “O tenzornykh kvadratakh neprivodimykh predstavlenii konechnykh pochti prostykh grupp. I”, Modelirovanie i analiz informatsionnykh sistem, 18:1 (2011), 130–141

[12] S. V. Polyakov, “O tenzornykh kvadratakh neprivodimykh predstavlenii pochti prostykh grupp s tsokolem, izomorfnym $L_2(q)$”, Vestnik Permskogo universiteta (to appear)