University of IsfahanInternational Journal of Group Theory2251-765010120210301A note on locally soluble almost subnormal subgroups in divsion rings39462381310.22108/ijgt.2019.116399.1546ENTruongHuu DungFaculty of Mathematics and Computer Science, VNUHCM-University of Science, 227 Nguyen Van Cu Str., Dist. 5,
HCM-City, Vietnam0000-0001-6552-724XJournal Article20190411Let $D$ be a division ring with center $F$ and assume that $N$ is a locally soluble almost subnormal subgroup of the multiplicative group $D^*$ of $D$. We prove that if $N$ is algebraic over $F$, then $N$ is central. This answers partially \cite[Conjecture 1]{hai_13}.https://ijgt.ui.ac.ir/article_23813_7fdc0ec932613c6a2824e6a33c1a11a8.pdf