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We show that the automorphism group of the countable universal distributive lattice has strong uncountable cofinality, and we adapt the method to deduce the strong uncountable cofinality of the automorphism group of the countable universal generalized boolean algebra.
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Czasopismo
Rocznik
Tom
Strony
473--479
Opis fizyczny
Bibliogr. 15 poz.
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autor
autor
- Institut Für Informatik University Of Leipzig 04009 Leipzig, Germany, droste@informatik.uni-leipzig.de
Bibliografia
- [1] R. D. Anderson, The algebraic simplicity of certain groups of homeomorphisms, Amer. J. Math. 80 (1958), 955–963.
- [2] G. M. Bergman, Generating infinite symmetric groups, Bull. London Math. Soc. 38 (2006), 429–440.
- [3] J. D. Dixon, P. M. Neumann, S. Thomas, Subgroups of small index in infinite permutation groups, Bull. London Math. Soc. 18 (1986), 580–586.
- [4] M. Droste, R. Göbel, Uncountable cofinalities of permutation groups, J. London Math. Soc. 71 (2005), 335–344.
- [5] M. Droste, W. C. Holland, Generating automorphism groups of chains, Forum Math. 17 (2005), 699–710.
- [6] M. Droste, D. Macpherson, The automorphism group of the universal distributive lattice, Algebra Universalis 43 (2000), 295–306.
- [7] M. Droste, J. K. Truss, Uncountable cofinalities of automorphism groups of linear and partial orders, Algebra Universalis 62 (2009), 75–90.
- [8] A. M. W. Glass, Ordered Permutation Groups, London Math. Soc. Lecture Notes No. 55 (1981), Cambridge University Press.
- [9] G. A. Grätzer, General Lattice Theory, 2nd edition, Birkhäuser Verlag, Basel, 2003.
- [10] C. Gourion, À propos du groupe des automorphismes de (Q,_), C. R. Acad. Sci. Paris 315 (1992), 1329–1331.
- [11] W. Hodges, Model Theory, Cambridge University Press, Cambridge, 1993.
- [12] A. S. Kechris, C. Rosendal, Turbulence, amalgamation, and generic automorphisms of homogeneous structures, Proc. London Math. Soc. 94 (2006), 302–350.
- [13] S. Koppelberg, J. Tits, Une propriété des produits directs infinis de groupes finis isomorphes, C. R. Acad. Sci. Paris 279 (1974), 583–585.
- [14] H. D. Macpherson, P. M. Neumann, Subgroups of infinite permutation groups, J. London Math. Soc. 42 (1990), 64–84.
- [15] S. Thomas, Cofinalities of infinite permutation groups, in: Advances in Algebra and Model Theory, edited byM. Droste and R. Göbel, Gordon and Breach, pages 101–120, 1997.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA4-0033-0012