On orbits of automorphism groups II
. Let G be a finite group, let A be a group of automorphisms of G and let C G ( A ) denote the subgroup of fixed points of A in G . If the order of C G ( A ) is coprime to the number of orbits of A in G , then C G ( A ) is contained in the autocommutator subgroup [ G , A ]. The notion of class-avoid...
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| Veröffentlicht in: | Archiv der Mathematik 2009-03, Vol.92 (3), p.200-205 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | .
Let
G
be a finite group, let
A
be a group of automorphisms of
G
and let
C
G
(
A
) denote the subgroup of fixed points of
A
in
G
. If the order of
C
G
(
A
) is coprime to the number of orbits of
A
in
G
, then
C
G
(
A
) is contained in the autocommutator subgroup [
G
,
A
]. The notion of class-avoiding automorphism is used to extend theorems of J. Thompson and P. Rowley. |
|---|---|
| ISSN: | 0003-889X 1420-8938 |
| DOI: | 10.1007/s00013-009-3082-9 |