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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
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Abstract

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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