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

Abstract

Almost simple SM_m-groups are considered. A group G is called a 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 SM_2-groups.

Keywords

• sr-groups
• sm_m-groups
• almost simple groups
• automorphisms
• gap