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Pàgina inicial > Articles > Articles publicats > On the fixed-point set of an automorphism of a group |
Data: | 2013 |
Resum: | Let Ø be an automorphism of a group G. Under variousfiniteness or solubility hypotheses, for example under polycyclicity, the commutator subgroup [G; Ø] has finite index in G if thefixed-point set CG(Ø) of Ø in G isfinite, but not conversely, even for polycyclic groups G. Here we consider a stronger, yet natural, notion of what it means for [G;Ø] to have finite index' in G and show that in many situations, including G polycyclic, it is equivalent to CG(Ø) being finite. |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió publicada |
Matèria: | Automorphism ; Xed-point set ; Soluble group |
Publicat a: | Publicacions matemàtiques, Vol. 57, Núm. 1 (2013) , p. 139-153, ISSN 2014-4350 |
15 p, 315.9 KB |