This article is cited in 2 papers

On tensor squares of irreducible representations of almost simple groups. I

S. V. Polyakov

P. G. Demidov Yaroslavl State University

Abstract: Almost simple $\mathrm{SM}_m$-groups are considered. A group $G$ is called a $\mathrm{SM}_m$-group if the tensor square of any irreducible representation is decomposed into the sum of its irreducible representations with multiplicities not greater than $m$. In the first part of this article we consider simple groups. It turned out that among them only groups $L_2(q)$, $q=2^t$, $t>1$, are $\mathrm{SM}_2$-groups.

Keywords: SR-groups, SM$_m$-groups, almost simple groups, automorphisms, GAP.

UDC: 517.51+514.17

Received: 22.01.2010

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