Bounds of the Group of IA-Automorphisms

Abstract

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 \( r \).