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On the fixed-point set of an automorphism of a group
Wehrfritz, B. A. F.

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 ; publishedVersion
Matèria: Automorphism ; Xed-point set ; Soluble group
Publicat a: Publicacions matemàtiques, Vol. 57, Núm. 1 (2013) , p. 139-153, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_57113_06

15 p, 315.9 KB

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