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