The prime-power hypothesis on the codegrees of irreducible characters.

AbstractFor a character <italic>χ</italic> of a finite group <italic>G</italic>, the number cod(χ)=[G:Kerχ]χ(1) is called the codegree of <italic>χ</italic>. In this paper, we show that if for every non-principal irreducible characters <italic>χ</italic> and ϕ of <italic>G</italic> with cod(χ)≠cod(ϕ), the greatest common divisor of cod(χ) and cod(ϕ) is a prime-power, then either <italic>G</italic> is solvable or G/Sol(G) is isomorphic to one of the groups Alt5 or PSL2(8), where Sol(G) is the solvable radical of the group <italic>G</italic>. [ABSTRACT FROM AUTHOR]