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  • Print publication year: 2018
  • Online publication date: February 2018

7 - Simon Smith's construction of an uncountable family of simple, totally disconnected, locally compact groups

[1] C.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 (2015), 235–261.
[2] M., Burger and S., Mozes, Groups acting on trees: from local to global structure, Publ. Math. IHES 92 (2000), 113–150.
[3] P.-E., Caprace and T. de, Medts, Simple locally compact groups acting on trees and their germs of automorphisms, Transformation Groups 16 (2011) 375–411.
[4] A.Y., Ol'shanskii, An infinite group with subgroups of prime orders, Math. USSR Izv. 16 (1981), 279–289; translation of Izvestia Akad. Nauk SSSR Ser. Matem. 44 (1980), 309–321.
[5] A.Y., Ol'shanskii, Groups of bounded period with subgroups of prime order, Algebra and Logic 21 (1983), 369–418; translation of Algebra i Logika 21 (1982), 553–618.
[6] J.-P., Serre, Trees, Springer-Verlag, 2003.
[7] S.M., Smith, A product for permutation groups and topological groups, Duke Math. J. 166(15) (2017), 2965–2999.
[8] J., Tits, Sur le groupe des automorphismes d'un arbre, in Essays on topology and related topics (Memoires dédiés a Georges de Rham), Springer, New York, 1970, pp. 188–211.
[9] V.V., Uspenskii, A universal topological group with a countable basis, Funct. Anal. and its Appl. 20 (1986), 86–87.