Classification of the simple factors appearing in composition series of totally disconnected contraction groups

Helge Glöckner 1  and George A. Willis 2
  • 1 Universität Paderborn, Institut für Mathematik, Warburger Str. 100, 33098 Paderborn, Germany. e-mail: glockner@math.upb.de
  • 2 Department of Mathematics, University of Newcastle, Callaghan, NSW 2308, Australia. e-mail: George.Willis@newcastle.edu.au

Abstract

Let G be a totally disconnected, locally compact group admitting a contractive automorphism α. We prove a Jordan-Hölder theorem for series of α-stable closed subgroups of G, classify all possible composition factors and deduce consequences for the structure of G.

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The Journal für die reine und angewandte Mathematik is the oldest mathematics periodical still in existence. Founded in 1826 by August Leopold Crelle and edited by him until his death in 1855, it soon became widely known under the name of Crelle’s Journal. In the 190 years of its existence, Crelle’s Journal has developed to an outstanding scholarly periodical with one of the worldwide largest circulations among mathematics journals.

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