Revista de la
Unión Matemática Argentina
Finite groups in which some maximal subgroups are MNP-groups
Pengfei Guo and Huaguo Shi

Volume 68, no. 2 (2025), pp. 423–435    

Published online (final version): August 19, 2025

https://doi.org/10.33044/revuma.4266

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Abstract

A finite group $G$ is called an MNP-group if all maximal subgroups of the Sylow subgroups of $G$ are normal in $G$. The aim of this paper is to give a necessary and sufficient condition for a group to be an MNP-group, characterize the structure of finite groups whose maximal subgroups (respectively, maximal subgroups of even order) are all MNP-groups, and determine finite non-abelian simple groups whose second maximal subgroups (respectively, maximal subgroups of even order) are all MNP-groups.

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