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
17 - The structure lattice of a totally disconnected locally compact group
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. 258 - 266Publisher: Cambridge University PressPrint publication year: 2018
References
[1] , and . Abstract commensurators of profinite groups. Trans. Amer. Math. Soc.
363 (2011), 5381–5417.
[2] , and . Locally normal subgroups of totally disconnected groups. Part I: General theory. Forum Math. Sigma 5 (2017), e11, 76 pp.
[3] , and . Locally normal subgroups of totally disconnected groups. Part II: Compactly generated simple groups. Forum Math. Sigma 5 (2017), e12, 89 pp.
[4] . Pseudo-complements in semi-lattices. Duke Math. J.
29 (1962), 505–514.
[5] . A course in the theory of groups, 2nd edn. (Springer, 1996).
[6] . Groups with every proper quotient finite. Proc. Cambridge Philos. Soc.
69 (1971), 373–391.
[7] . Structure theory for branch groups. In Geometric and Homological Topics in Group Theory, London Math. Soc. Lecture Note Ser. 358 (Cambridge University Press, 2009), 306–320.
[8] . Profinite groups (Clarendon Press, Oxford, 1998).