Finite groups whose codegrees are almost prime.

For a character χ of a finite group G, the number cod (χ) = | G : ker (χ) | / χ (1) is called the codegree of χ. In this paper we show that if G is nonsolvable, then the codegree graph Γ (G) has a triangle. Also by using this result we show that if G has one composite codegree, then G is solvable and | cod (G) | ≤ 5. [ABSTRACT FROM AUTHOR]