On division subrings normalized by almost subnormal subgroups in\n division rings

Let $D$ be a division ring with infinite center, $K$ a proper division\nsubring of $D$ and $N$ an almost subnormal subgroup of the multiplicative group\n$D^*$ of $D$. The aim of this paper is to show that if $K$ is $N$-invariant and\n$N$ is non-central, then $K$ is central. Some examples of almost subnormal\nsubgroups in division rings that are not subnormal are also given.\n