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Monothetic algebraic groups

Part of: Abelian groups Linear algebraic groups and related topics Algebraic groups

Published online by Cambridge University Press:  09 April 2009

Giovanni Falcone ,
Peter Plaumann  and
Karl Strambach
Giovanni Falcone
Affiliation:
Dipartimento di Metodi e Modelli MatematiciUniversità di Palermoviale delle Scienze1-90128 PalermoItalygfalcone@unipa.it
Peter Plaumann
Affiliation:
Mathematisches InstitutUniversität ErlangenBismarckstraße 1 ½D-91054 ErlangenGermanyplaumann@mi.uni-erlangen.destrambach@mi.uni-erlangen.de
Karl Strambach
Affiliation:
Mathematisches InstitutUniversität ErlangenBismarckstraße 1 ½D-91054 ErlangenGermanyplaumann@mi.uni-erlangen.destrambach@mi.uni-erlangen.de
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Abstract

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We call an algebraic group monothetic if it possesses a dense cyclic subgroup. For an arbitrary field k we describe the structure of all, not necessarily affine, monothetic k-groups G and determine in which cases G has a k-rational generator.

MSC classification

Secondary: 14L99: None of the above, but in this section 20G15: Linear algebraic groups over arbitrary fields 20K99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 82 , Issue 3 , June 2007 , pp. 315 - 324
Copyright
Copyright © Australian Mathematical Society 2007

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