Geodesic
Finite groups whose prime graphs do not contain triangles. II
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 3-13
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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.
Keywords: finite group, fitting length, prime graph.
Mots-clés : non-solvable group, solvable group 
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O. A. Alekseeva; A. S. Kondrat'ev. Finite groups whose prime graphs do not contain triangles. II. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 3-13. http://geodesic.mathdoc.fr/item/TIMM_2016_22_1_a0/

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