2018
Том 70
№ 7

# On some groups all subgroups of which are nearly pronormal

Abstract

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 $G$ are pronormal.

English version (Springer): Ukrainian Mathematical Journal 59 (2007), no. 10, pp 1493-1500.

Citation Example: Kurdachenko L. A., Russo A., Vincenzi G. On some groups all subgroups of which are nearly pronormal // Ukr. Mat. Zh. - 2007. - 59, № 10. - pp. 1331–1338.

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