Automorphisms of groups and converse of Schur's theorem
Group Theory
2013-03-21 v1
Abstract
An automorphism of a group G is called an IA-automorphism if it induces the identity automorphism on the abelianized group G/G'. Let IA(G) denote the group of all IA-automorphisms of G. We classify all finitely generated nilpotent groups G of class 2 for which IA(G) is isomorphic to Inn(G). In particular, we classify all finite nilpotent groups of class 2 for which each IA-automorphism is inner. As consequences, we give surprisingly very easy proofs of converse of Schur's theorem and also prove some other related results.
Keywords
Cite
@article{arxiv.1303.4966,
title = {Automorphisms of groups and converse of Schur's theorem},
author = {Deepak Gumber and Hemant Kalra and Sandeep Singh},
journal= {arXiv preprint arXiv:1303.4966},
year = {2013}
}
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9 pages