Geodesic
Finite groups in which all $2$-maximal subgroups are $\pi$-decomposable
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 29-43

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Let $\pi$ is a set of prime numbers. A very broad generalization of notion of nilpotent group is the notion of $\pi$-decomposable group, i.e. the direct product of $\pi$-group and $\pi'$-group. In the paper, the description of the finite non-$\pi$-decomposable groups in which all $2$-maximal subgroups are $\pi$-decomposable is obtained. The proof used the author's results connected with the notion of control the prime spectrum of finite simple groups. The finite nonnilpotent groups in which all $2$-maximal subgroups are nilpotent was studied by Z. Janko in 1962 in case of nonsolvable groups and the author in 1968 in case of solvable groups.
Keywords: finite group, maximal subgroup, control of prime spectrum of group.
Mots-clés : simple group, $\pi$-decomposable group 
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     author = {V. A. Belonogov},
     title = {Finite groups in which all $2$-maximal subgroups are $\pi$-decomposable},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {29--43},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2014_20_2_a2/}
}
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V. A. Belonogov. Finite groups in which all $2$-maximal subgroups are $\pi$-decomposable. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 29-43. http://geodesic.mathdoc.fr/item/TIMM_2014_20_2_a2/