A Note on I-Automorphisms

✍ Scribed by J.C. Beidleman; H. Heineken

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 113 KB
• Volume: 234
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2000.8534

✦ Synopsis

dedicated to professor helmut wielandt on the occasion of his 90th birthday

1. INTRODUCTORY REMARKS

Let G be a group and denote by PAut G the group of power automorphisms of G (see [4]). An automorphism of G is called an I-automorphism of G if it maps every infinite subgroup of G onto itself. The set IAut G of all I-automorphisms of G is a normal subgroup of Aut G containing PAut G . IAut G has been investigated by Curzio et al. [5], where they often consider the case when IAut G = PAut G or at least IAut G is abelian.

Here we consider the structural restriction on G when IAut G = PAut G . One of the major outcomes of this work is that for many groups H in fact IAut H = PAut H holds. We also characterize infinite Chernikov groups G for which IAut G = PAut G .