Let D be a division ring, n a positive integer, and GLn(D) the general linear group of degree n over D
Nearby in the stack
. 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