Finite groups whose prime graphs do not contain triangles. II

The study of finite groups whose prime graphs do not contain triangles is continued. The main result of the given part of the work is the following theorem: if $G$ is a finite non-solvable group whose prime graph does not contain triangles and $S(G)$ is the greatest solvable normal subgroup in $G$ then $|\pi(G)|\leq 8$ and $|\pi(S(G))|\leq 3$. Furthermore, a detailed description of the structure of a group $G$ satisfying the conditions of the theorem in the case when $\pi(S(G))$ contains a number which does not divide the order of the group $G/S(G)$. It is also constructed an example of a finite solvable group with the Fitting length 5 whose prime graph is 4-cycle. This completes the determination of exact bound for the Fitting length of finite solvable groups whose prime graphs do not contain triangles.