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Bounds of the group of $IA$-automorphisms

R. G. Ghumde^a, S. H. Ghate<sup>b

a</sup> Department of Mathematics, Ramdeobaba College of Engineering & Management, 440013, Nagpur, India
^b Department of Mathematics, R.T.M. Nagpur University, 440033, Nagpur, India

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 $r$.

Keywords and phrases: $IA$-automorphism, finitely generated group.

MSC: 20D45, 20D15

Received: 28.03.2016

Language: English

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