Geodesic
Simple non-abelian groups with second maximal pronormal subgroups
Problemy fiziki, matematiki i tehniki, no. 3 (2019), pp. 104-106

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V.I. Zenkov put in the Kourovskaya notebook the following problem 19.109: is it true that in a non-abelian finite simple group $G$ all maximal subgroups are Hall subgroups if and only if every second maximal subgroup is pronormal in $G$? This paper shows that this problem is solved negatively.
Keywords: finite group, second maximal subgroup, pronormal subgroup. 
@article{PFMT_2019_3_a17,
     author = {V. N. Tyutyanov},
     title = {Simple non-abelian groups with second maximal pronormal subgroups},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {104--106},
     publisher = {mathdoc},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2019_3_a17/}
}
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V. N. Tyutyanov. Simple non-abelian groups with second maximal pronormal subgroups. Problemy fiziki, matematiki i tehniki, no. 3 (2019), pp. 104-106. http://geodesic.mathdoc.fr/item/PFMT_2019_3_a17/