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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 |
