The central kernel K(G) of a group G is the subgroup consisting of all elements fixed by every central automorphism of G. It is proved here that if G is a finite-by- nilpotent group whose central kernel has finite index, the G is finite over the centre, and the elements of finite order of G form a finite subgroup; in particular G is finite, provided that it is periodic. Moreover, if G is a periodic finite-b-nilpotent group and G/K(G) is a Cernikov group, it turns out that G itself is a Cernikov group.

On fixed points of central automorphisms of finite-by-nilpotent groups

CATINO, Francesco;MICCOLI, Maria Maddalena
2014-01-01

Abstract

The central kernel K(G) of a group G is the subgroup consisting of all elements fixed by every central automorphism of G. It is proved here that if G is a finite-by- nilpotent group whose central kernel has finite index, the G is finite over the centre, and the elements of finite order of G form a finite subgroup; in particular G is finite, provided that it is periodic. Moreover, if G is a periodic finite-b-nilpotent group and G/K(G) is a Cernikov group, it turns out that G itself is a Cernikov group.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11587/386282
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