$IA$-automorphisms of $p$-groups, finite polycyclic groups and other results

R. G. Ghumde; S. H. Ghate

Authors

R. G. Ghumde Department of Mathematics, Ramdeobaba College of Engineering & Management, Nagpur, India 440013 Author
S. H. Ghate Department of Mathematics, R.T.M. Nagpur University, Nagpur, India 440033 Author

Keywords:

Central automorphism,

I A

-automorphism,

p

-groups

Subjects:

20D45, 20D10, 20D15

Abstract

In this paper, the group $I A (G)$ of all $I A$ -automorphisms of a group $G$ is studied.We prove some results regarding non-triviality, polycyclicity and commutativity of $I A (G)$ in additionto proving some basic results. We also prove some results analogous to a result by Schur and a weak formof its converse in the context of $I A$ -automorphisms.

$I A$ -automorphisms of $p$ -groups, finite polycyclic groups and other results

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IA-automorphisms of p-groups, finite polycyclic groups and other results

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$I A$ -automorphisms of $p$ -groups, finite polycyclic groups and other results