On some groups all subgroups of which are nearly pronormal

• Date: 2007
• Main Authors: Vincenzi, G., Kurdachenko, L. A., Russo, A., Винчензи, Дж., Курдаченко, Л. А., Руссо, А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2007
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3392
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

A subgroup $H$ of a group $G$ is said to be nearly pronormal in $G$ if, for each subgroup $L$ of the group $G$ including H, the normalizer $N_L ( H)$ is contranormal in $L$. We prove that if $G$ is a (generalized) soluble group in which every subgroup is nearly pronormal, then all subgroups of $G$ a...