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3.14 (1969)

Solved

Let $G$ be a finite group of $n \times n$ matrices over a skew field $T$ of characteristic zero. Prove that $G$ has a soluble normal subgroup $H$ whose index in $G$ is not greater than some number $f(n)$ not depending on $G$ or $T$. This problem is related to the representation theory of finite groups (the Schur index).

Contributor: A. E. Zalesskiĭ

Progress

This is proved mod CFSG (B. Hartley, M. A. Shahabi Shojaei, Math. Proc. Cambridge Phil. Soc., 92 (1982), 55–64).

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