On tensor squares of reducible representations of almost simple groups. II

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 $G\cong PGL_2(q)$.