A note on locally soluble almost subnormal subgroups in divsion rings

Let $D$ 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 ۱]{hai_۱۳}‎.

Keywords:

‎Division ring‎ , ‎almost subnormal subgroup‎ , ‎locally soluble