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20.38 (2022)

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Suppose that $H$ is an almost simple group of Lie type and $G$ is a finite group such that $G$ and $H$ have the same sets of degrees of irreducible complex characters. Must there exist an abelian normal subgroup $A$ of $G$ such that $G/A$ is isomorphic to $H$?

Contributor: A. Iranmanesh

Progress

Comment of 2025: The conjecture was confirmed for projective general linear and unitary groups of dimension 3 (F. Shirjian, A. Iranmanesh, Illinois J. Math., 64, no. 1 (2020), 49–69).

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