Book contents
- Frontmatter
- Contents
- Foreword
- 1 On the role of totally disconnected groups in the structure of locally compact groups
- 2 Locally compact groups as metric spaces
- 3 A short primer on profinite groups
- 4 Lectures on Lie groups over local fields
- 5 Abstract quotients of profinite groups, after Nikolov and Segal
- 6 Automorphism groups of trees: generalities and prescribed local actions
- 7 Simon Smith's construction of an uncountable family of simple, totally disconnected, locally compact groups
- 8 The Neretin groups
- 9 The scale function and tidy subgroups
- 10 Contraction groups and the scale
- 11 The Bader–Shalom normal subgroup theorem
- 12 Burger–Mozes’ simple lattices
- 13 A lecture on invariant random subgroups
- 14 L2-Betti number of discrete and non-discrete groups
- 15 Minimal normal closed subgroups in compactly generated tdlc groups
- 16 Elementary totally disconnected locally compact groups, after Wesolek
- 17 The structure lattice of a totally disconnected locally compact group
- 18 The centraliser lattice
- 19 On the quasi-isometric classification of locally compact groups
- 20 Future directions in locally compact groups: a tentative problem list
- Index
- References
9 - The scale function and tidy subgroups
Published online by Cambridge University Press: 05 February 2018
Book contents
- Frontmatter
- Contents
- Foreword
- 1 On the role of totally disconnected groups in the structure of locally compact groups
- 2 Locally compact groups as metric spaces
- 3 A short primer on profinite groups
- 4 Lectures on Lie groups over local fields
- 5 Abstract quotients of profinite groups, after Nikolov and Segal
- 6 Automorphism groups of trees: generalities and prescribed local actions
- 7 Simon Smith's construction of an uncountable family of simple, totally disconnected, locally compact groups
- 8 The Neretin groups
- 9 The scale function and tidy subgroups
- 10 Contraction groups and the scale
- 11 The Bader–Shalom normal subgroup theorem
- 12 Burger–Mozes’ simple lattices
- 13 A lecture on invariant random subgroups
- 14 L2-Betti number of discrete and non-discrete groups
- 15 Minimal normal closed subgroups in compactly generated tdlc groups
- 16 Elementary totally disconnected locally compact groups, after Wesolek
- 17 The structure lattice of a totally disconnected locally compact group
- 18 The centraliser lattice
- 19 On the quasi-isometric classification of locally compact groups
- 20 Future directions in locally compact groups: a tentative problem list
- Index
- References
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- New Directions in Locally Compact Groups , pp. 145 - 160Publisher: Cambridge University PressPrint publication year: 2018
References
[1] , Dense orbits of automorphisms and compactness of groups, Topology Appl.
20 (1985), no. 1, 1–15.
[2] , Lectures on ergodic theory, Chelsea Publishing Co., New York, 1960.
[3] and , Abstract harmonic analysis. Vol. I, second ed., Grundlehren der Mathematischen Wissenschaften, vol. 115, Springer-Verlag, Berlin-New York, 1979.
[4] öller, Structure theory of totally disconnected locally compact groups via graphs and permutations, Canad. J. Math. 54 (2002), no. 4, 795–827.
[5] and , Dense orbits and compactness of groups, Bull. Austral. Math. Soc.
68 (2003), no. 1, 155–159.
[6] , Ergodic properties of automorphisms of a locally compact group, Proc. Amer. Math. Soc.
17 (1966), 372–376.
[7] , A course on totally disconnected locally compact Polish groups, unpublished notes (2014) available at http://people.math.binghamton.edu/wesolek/.
[8] , The structure of totally disconnected, locally compact groups, Math. Ann.
300 (1994), no. 2, 341–363.
[9] , Totally disconnected groups and proofs of conjectures of Hofmann and Mukherjea, Bull. Austral. Math. Soc.
51 (1995), no. 3, 489–494.
[10] , Further properties of the scale function on a totally disconnected group, J. Algebra
237 (2001), no. 1, 142–164.
[11] , The scale and tidy subgroups for endomorphisms of totally disconnected locally compact groups, Math. Ann.
361 (2015), no. 1-2, 403–442.