Huppert's conjecture for character codegrees

Abstract Huppert's ρ‐σ conjecture is one of the main open problems on character degrees finite groups. A number have been studied. For instance, T. Keller and J. Zhang considered problem for element orders in 1990s. Recently, a lot research being done codegrees. Y. Yang G. Qian studied codegrees 2017. In this note, we obtain sharp bound groups with trivial solvable radical. As consequence, improve general Qian. groups, notice that very closely related to orders. particular, give partial negative answer speculation by exact