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17.53 (2010)

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A finite group $G$ is called simply reducible (SR-group) if every element of $G$ is conjugate to its inverse, and the tensor product of any two irreducible representations of $G$ decomposes into a sum of irreducible representations of $G$ with coefficients 0 or 1.
$\qquad$ a) Is it true that the nilpotent length of a soluble SR-group is at most 5?
$\qquad$ b) Is it true that the derived length of a soluble SR-group is bounded by some constant $c$?

Contributor: L. S. Kazarin

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