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Oct 26, 2018 at 13:29 comment added MathManiac @PeterMcNamara Well spotted, and nice fix!
Oct 26, 2018 at 8:14 comment added Peter McNamara This can be fixed by replacing V with $V\oplus (V\otimes V)$ to say WLOG V is projectively faithful, then the argument goes through.
Oct 26, 2018 at 6:41 comment added Peter McNamara The conclusion that $|\chi(g)|\leq a-\epsilon$ does not follow if g is central. For a concrete example, suppose G is cyclic. This proof does not work as written for such groups.
Oct 26, 2018 at 6:00 history edited YCor CC BY-SA 4.0
formatting
Oct 26, 2018 at 4:27 history answered MathManiac CC BY-SA 4.0