Locally normal subgroups of totally disconnected groups. Part II: Compactly generated simple groups

Forum of Mathematics, Sigma

Volumn 5, Issue , 2017, Pages

  Caprace, Pierre Emmanuel ^a   Reid, Colin D ^b   Willis, George A ^b  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^b UNIVERSITY OF NEWCASTLE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85047376880     PISSN: None     EISSN: 20505094     Source Type: Journal    
DOI: 10.1017/fms.2017.8     Document Type: Article

References (72)

1. H. Abels, 'Kompakt definierbare topologische Gruppen', Math. Ann. 197 (1972), 221-233.
2. H. Abels, 'Specker-Kompaktifizierungen von lokal kompakten topologischen Gruppen', Math. Z. 135 (1974), 325-361.
3. R. Arens, 'Topologies for homeomorphism groups', Amer. J. Math. 68 (1946), 593-610.
4. C. Banks, M. Elder and G. A. Willis, 'Simple groups of automorphisms of trees determined by their actions on finite subtrees', J. Group Theory 18(2) (2015), 235-261.
5. Y. Barnea, M. Ershov and T. Weigel, 'Abstract commensurators of profinite groups', Trans. Amer. Math. Soc. 363(10) (2011), 5381-5417.
6. U. Baumgartner, J. Ramagge and B. Rémy, 'Contraction groups in complete Kac-Moody groups', Groups Geom. Dyn. 2(3) (2008), 337-352.
7. U. Baumgartner and G. A. Willis, 'Contraction groups and scales of automorphisms of totally disconnected locally compact groups', Israel J. Math. 142 (2004), 221-248.
8. V. V. Belyaev, 'Locally finite groups with a finite nonseparable subgroup (Russian) Sibirsk', Mat. Ž. 34(2) (1993), 23-41. 226, 233.
9. Translation in Siberian Math. J. 34 (1993), no. 2, 218-232 (1994).
10. R. Bieri and R. Strebel, On Groups of PL-Homeomorphisms of the Real Line, Mathematical Surveys and Monographs, 215 (American Mathematical Society, Providence, RI, 2016).
11. A. Borel and J. Tits, 'Homomorphismes 'abstraits' de groupes algébriques simples', Ann. of Math. 97 (1973), 499-571.
12. N. Bourbaki, 'Groupes et algèbres de Lie', in Chapitre II: Algèbres de Lie libres. Chapitre III: Groupes de Lie, Actualités Scientifiques et Industrielles, 1349 (Hermann, Paris, 1972), 320.
13. A. Bouziad and J.-P. Troallic, 'Some remarks about strong proximality of compact flows', Colloq. Math. 115(2) (2009), 159-170.
14. F. Bruhat and J. Tits, 'Groupes réductifs sur un corps local', Publ. Math. Inst. Hautes Études Sci. 41 (1972), 5-251.
15. M. Burger and Sh. Mozes, 'Groups acting on trees: from local to global structure', Publ. Math. Inst. Hautes Études Sci. 92 (2000), 113-150.
16. P.-E. Caprace, 'Automorphism groups of right-angled buildings: simplicity and local splittings', Fund. Math. 224 (2014), 17-51.
17. P.-E. Caprace and T. De Medts, 'Simple locally compact groups acting on trees and their germs of automorphisms', Transform. Groups 16(2) (2011), 375-411.
18. P.-E. Caprace and T. De Medts, 'Trees, contraction groups, and Moufang sets', Duke Math. J. 162(13) (2013), 2413-2449.
19. P.-E. Caprace and N. Monod, 'Decomposing locally compact groups into simple pieces', Math. Proc. Cambridge Philos. Soc. 150(1) (2011), 97-128.
20. P.-E. Caprace, C. D. Reid and G. A. Willis, 'Locally normal subgroups of simple locally compact groups', C. R. Acad. Sci. Paris Ser. I 351(17-18) (2013), 657-661.
21. P.-E. Caprace, C. D. Reid and G. A. Willis, 'Limits of contraction groups and the Tits core', J. Lie Theory 24(4) (2014), 957-967.
22. P.-E. Caprace, C. D. Reid and G. A. Willis, 'Locally normal subgroups of totally disconnected groups; Part I: general theory', Forum of Mathematics, Sigma 5 (2017), doi:10.1017/fms.2017.9.
23. P.-E. Caprace and T. Stulemeijer, 'Totally disconnected locally compact groups with a linear open subgroup', Int. Math. Res. Not. IMRN 24 (2015), 13800-13829.
24. R. Cluckers, Y. Cornulier, N. Louvet, R. Tessera and A. Valette, 'The Howe-Moore property for real and p-adic groups', Math. Scand. 109(2) (2011), 201-224.
25. Y. Cornulier and P. de la Harpe, Metric Geometry of Locally Compact Groups, EMS Tracts in Mathematics, 25 (European Math. Soc., Zurich, 2016).
26. T. De Medts, A. C. Silva and K. Struyve, 'Universal groups for right-angled buildings', Preprint, 2016, arXiv:1603.04754.
27. D. B. A. Epstein, 'The simplicity of certain groups of homeomorphisms', Compos. Math. 22 (1970), 165-173.
28. H. Furstenberg, 'Boundary theory and stochastic processes on homogeneous spaces', in Harmonic Analysis on Homogeneous Spaces, Proc. Sympos. Pure Math., XXVI (Williams Coll., Williamstown, Mass., 1972) (Amer. Math. Soc., Providence, RI, 1973), 193-229.
29. A. Garrido, 'On the congruence subgroup problem for branch groups', Israel J. Math. 216(1) (2016), 1-13.
30. S. Glasner, 'Topological dynamics and group theory', Trans. Amer. Math. Soc. 187 (1974), 327-334.
31. K. W. Gruenberg, 'Residual properties of infinite soluble groups', Proc. Lond. Math. Soc. 7(3) (1957), 29-62.
32. F. Haglund and F. Paulin, 'Simplicité de groupes d'automorphismes d'espaces à courbure négative', in The Epstein Birthday Schrift, Geom. Topol. Monogr., 1 (Geom. Topol. Publ., Coventry, 1998), 181-248. (electronic).
33. K. Juschenko and N. Monod, 'Cantor systems, piecewise translations and simple amenable groups', Ann. of Math. (2) 178(2) (2013), 775-787.
34. S. Kakutani and K. Kodaira, 'Über das Haarsche Mass in der lokal bikompakten Gruppe', Proc. Imp. Acad. Tokyo 20 (1944), 444-450.
35. C. Kapoudjian, 'Simplicity of Neretin's group of spheromorphisms', Ann. Inst. Fourier (Grenoble) 49(4) (1999), 1225-1240.
36. L. Kramer, 'The topology of a semisimple Lie group is essentially unique', Adv. Math. 228(5) (2011), 2623-2633.
37. N. Lazarovich, 'On regular CAT(0) cube complexes', Preprint, 2014, arXiv:1411.0178.
38. A. Le Boudec, 'Adrien Groups acting on trees with almost prescribed local action', Comment. Math. Helv. 91(2) (2016), 253-293.
39. A. Malcev, 'On isomorphic matrix representations of infinite groups', Mat. Sb. 8(50) (1940), 405-422 (Russian).
40. G. Margulis, Discrete Subgroups of Semi-Simple Lie Groups, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 17 (Springer, Berlin, 1991).
41. T. Marquis, 'Abstract simplicity of locally compact Kac-Moody groups', Compos. Math. 150(4) (2014), 713-728.
42. R. Möller and J. Vonk, 'Normal subgroups of groups acting on trees and automorphism groups of graphs', J. Group Theory 15(6) (2012), 831-850.
43. N. Monod, Continuous Bounded Cohomology of Locally Compact Groups, Lecture Notes in Mathematics, 1758 (Springer, Berlin, 2001).
44. D. Montgomery and L. Zippin, Topological Transformation Groups, (Interscience Publishers, New York-London, 1955).
45. V. Nekrashevych, 'Finitely presented groups associated with expanding maps'. Preprint, 2013, arXiv:1312.5654.
46. V. Nekrashevych, 'Palindromic subshifts and simple periodic groups of intermediate growth', Preprint, 2016, arXiv:1601.01033.
47. Yu. A. Neretin, 'On combinatorial analogs of the group of diffeomorphisms of the circle', Izv. Math. 41(2) (1993), 337-349 (Russian).
48. N. Nikolov, 'Algebraic properties of profinite groups', Preprint, 2011, arXiv:1108.5130.
49. N. Nikolov and D. Segal, 'Generators and commutators in finite groups; abstract quotients of compact groups', Invent. Math. 190(3) (2012), 513-602.
50. C. D. Reid and P. Wesolek, 'Homomorphisms into totally disconnected, locally compact groups with dense image', Preprint, 2015, arXiv:1509.00156v1.
51. C. D. Reid and P. Wesolek, 'The essentially chief series of a compactly generated locally compact group', Preprint, 2015, arXiv:1509.06593v4.
52. B. Rémy, 'Topological simplicity, commensurator superrigidity and non-linearities of Kac-Moody groups', Geom. Funct. Anal. 14(4) (2004), 810-852.With an appendix by P. Bonvin.
53. B. Rémy and M. Ronan, 'Topological groups of Kac-Moody type, right-angled twinnings and their lattices', Comment. Math. Helv. 81(1) (2006), 191-219.
54. L. Ribes and P. Zalesskii, Profinite Groups, 2nd edn, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], 40 (Springer, Berlin, 2010).
55. C. Riehm, 'The congruence subgroup problem over local fields', Amer. J. Math. 92 (1970), 771-778.
56. M. Rosenlicht, 'On a result of Baer', Proc. Amer. Math. Soc. 13 (1962), 99-101.
57. M. Rubin, 'On the reconstruction of topological spaces from their groups of homeomorphisms', Trans. Amer. Math. Soc. 312(2) (1989), 487-538.
58. J. Schur, 'Über die Darstellung der endlichen Gruppen durch gebrochen lineare Substitutionen', J. Reine Angew. Math. 127 (1904), 20-50.
59. Y. Shalom and G. A. Willis, 'Commensurated subgroups of arithmetic groups, totally disconnected groups and adelic rigidity', Geom. Funct. Anal. 23(5) (2013), 1631-1683.
60. S. M. Smith, 'A product for permutation groups and topological groups', Preprint, 2015, arXiv:1407.5697v2.
61. S. Thomas and B. Velickovic, 'On the complexity of the isomorphism relation for finitely generated groups', J. Algebra 217(1) (1999), 352-373.
62. J. Tits, 'Algebraic and abstract simple groups', Ann. of Math. 80 (1964), 313-329.
63. J. Tits, 'Sur le groupe des automorphismes d'un arbre', in Essays on Topology and Related Topics (Mémoires dédiés à Georges de Rham) (Springer, New York, 1970), 188-211.
64. J. Tits, 'Reductive groups over local fields', in Automorphic Forms, Representations and L-Functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 1, Proc. Sympos. Pure Math., XXXIII (Amer. Math. Soc., Providence, RI, 1979), 29-69.
65. J. Tits, 'Uniqueness and presentation of Kac-Moody groups over fields', J. Algebra 105(2) (1987), 542-573.
66. V. I. Ušakov, 'Topological FC-groups', Sibirsk. Mat. Ž. 4 (1963), 1162-1174.
67. S. P. Wang, 'Compactness properties of topological groups', Trans. Amer. Math. Soc. 154 (1971), 301-314.
68. P. Wesolek, 'Elementary totally disconnected locally compact groups', Proc. Lond. Math. Soc. 110(6) (2015), 1387-1434.
69. P. Wesolek, 'Commensurated subgroups in finitely generated branch groups', J. Group Theory 20(2) (2017), 385-392.
70. G. A. Willis, 'The number of prime factors of the scale function on a compactly generated group is finite', Bull. Lond. Math. Soc. 33(2) (2001), 168-174.
71. G. A. Willis, 'Compact open subgroups in simple totally disconnected groups', J. Algebra 312(1) (2007), 405-417.
72. G. A. Willis, 'The nub of an automorphism of a totally disconnected, locally compact group', Ergodic Theory Dynam. Systems 34(4) (2014), 1365-1394.