Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-15T06:53:28.770Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite groups with small automizers of their nonabelian subgroups

Published online by Cambridge University Press:  19 July 2001

ROLF BRANDL  and
MARIAN DEACONESCU
ROLF BRANDL
Affiliation:
Mathematisches Institut der Universität, Am Hubland 12, D-97074 Würzburg, Germany
MARIAN DEACONESCU
Affiliation:
Department of Mathematics, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let G be a group and let H be a subgroup of G. The automizer AutG(H) of H in G is defined as the group of automorphisms of H induced by conjugation of elements of NG(H). Thus AutG(H)≅NG(H)/CG(H), and we obviously have $$\tfrm{In(}H\tfrm{)≤Aut}_{G}\tfrm{(}H\tfrm{)≤Aut(}H\tfrm{).}$$ We call AutG(H) large if AutG(H)=Aut(H) and small if AutG(H)=In(H).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 41 , Issue 1 , March 1999 , pp. 59 - 64
Copyright
1999 Glasgow Mathematical Journal Trust