Abstract.  

Let G be a finite p-group. There is a well known conjecture that states,

If G is non-cyclic and of order pn, n ≥ 3, then |G| divides |Aut(G)|.

While the conjecture is known to be true for several classes of p-groups, it is not known in general. We shall discuss some recent work of Yadav which proves the result for a p-group, G, such that (G, Z(G)) is a Camina pair.