Bounds of the group of $IA$-automorphisms

In this paper, expressions for the lower and upper bounds on the number of $IA$-automorphisms of a finitely generated group have been obtained. Using these bounds a few results including the one by Yadav and Vermani on Hasse principle have been derived as simple corollaries. Considering groups of order $pq$, $pqr$ and $p^2q$ the exact number of $IA$-automorphisms have been obtained in terms of the distinct primes $p$, $q$ and $r$.