@article {
author = {Kurdachenko, Leonid and Longobardi, Patrizia and Maj, Mercede},
title = {On some groups whose subnormal subgroups are contranormal-free},
journal = {International Journal of Group Theory},
volume = {},
number = {},
pages = {-},
year = {2024},
publisher = {University of Isfahan},
issn = {2251-7650},
eissn = {2251-7669},
doi = {10.22108/ijgt.2024.139136.1871},
abstract = {If $G$ is a group, a subgroup $H$ of $G$ is said to be contranormal in $G$ if $H^G = G$, where $H^G$ is the normal closure of $H$ in $G$. We say that a group is contranormal-free if it does not contain proper contranormal subgroups. Obviously, a nilpotent group is contranormal-free. Conversely, if $G$ is a finite contranormal-free group, then $G$ is nilpotent. We study (infinite) groups whose subnormal subgroups are contranormal-free. We prove that if $G$ is a group which contains a normal nilpotent subgroup $A$ such that $G/A$ is a periodic Baer group, and every subnormal subgroup of $G$ is contranormal-free, then $G$ is generated by subnormal nilpotent subgroups; in particular $G$ is a Baer group. Furthermore, if $G$ is a group which contains a normal nilpotent subgroup $A$ such that the $0$-rank of $A$ is finite, the set $\Pi(A)$ is finite, $G/A$ is a Baer group, and every subnormal subgroup of $G$ is contranormal-free, then $G$ is a Baer group.},
keywords = {contranormal subgroups,subnormal subgroups,Nilpotent groups,hypercentral groups,upper central series},
url = {https://ijgt.ui.ac.ir/article_28378.html},
eprint = {https://ijgt.ui.ac.ir/article_28378_bec3ddac3956ad7f8cf5f6aed206c552.pdf}
}