Geodesic
On the solvability of a finite group with a pair of non-conjugate subgroups of primary indices~II
Problemy fiziki, matematiki i tehniki, no. 1 (2019), pp. 61-64.

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The solvability of a finite group $G$ with two non-conjugate maximal subgroups $A$ and $B$ that satisfy the following requirements has been proved: subgroups $A$ and $B$ have primary indices in $G$; all proper subgroups of $A$ and $B$ are $2$-nilpotent. In addition, if $G$ is $S_4$-free and the indices of the subgroups $A$ and $B$ are coprime, then the $2$-nilpotency of the subgroups $A$ and $B$ can be replaced by their solvability.
Keywords: finite group, maximal subgroup, $2$-nilpotent subgroup, non-conjugate subgroups, primary index.
Mots-clés : solvable group 
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V. S. Monakhov; D. A. Khadanovich. On the solvability of a finite group with a pair of non-conjugate subgroups of primary indices~II. Problemy fiziki, matematiki i tehniki, no. 1 (2019), pp. 61-64. http://geodesic.mathdoc.fr/item/PFMT_2019_1_a10/

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