Geodesic
On the solvability of finite groups with given cofactors of the maximal subgroups
Trudy Instituta matematiki, Tome 19 (2011) no. 2, pp. 60-68

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We consider a finite group such that the cofactor of every maximal subgroup is either group of odd order, or nilpotent group, or group with cyclic Sylow subgroups. The solvability of such group is obtained. 
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     author = {I. V. Lemeshev and V. S. Monakhov},
     title = {On the solvability of finite groups with given cofactors of the maximal subgroups},
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I. V. Lemeshev; V. S. Monakhov. On the solvability of finite groups with given cofactors of the maximal subgroups. Trudy Instituta matematiki, Tome 19 (2011) no. 2, pp. 60-68. http://geodesic.mathdoc.fr/item/TIMB_2011_19_2_a6/