  Let $D$ be a division ring, $n$ a positive integer, and GL$_n(D)$ the general
linear group of degree $n$ over $D$. In this paper, we study the induced
subgraph of the intersection graph of GL$_n(D)$ generated by all non-trivial
proper almost subnormal subgroups of GL$_n(D)$. We show that this subgraph is
complete if it is non-null. This property will be used to study subgroup
structure of a division ring. In particular, we prove that every non-central
almost subnormal subgroup of the multiplicative group $D^*$ of a division ring
$D$ contains a non-central subnormal subgroup of $D^*$.
