The Scale, Tidy Subgroups and Flat Groups

  • George WillisEmail author
Part of the MATRIX Book Series book series (MXBS, volume 1)


These notes discuss the scale, tidy subgroups, subgroups associated with endomorphisms and flat groups on totally disconnected locally compact (t.d.l.c) groups. The first section discusses the structure theory of subgroups which are minimizing for an endomorphism and introduces the scale of an endomorphism. The second section discusses the applications and properties of the scale function. Section 3 discusses other subgroups which may be associated with endomorphisms in a unique way. Section 4 discusses flat groups of automorphisms, the flat rank and various results about flat groups. The final section discusses the geometry of t.d.l.c groups.


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We would like to thank Stephan Tornier, who prepared some of the figures used in these lecture notes.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of NewcastleCallaghanAustralia

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