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Tytuł artykułu

Sierpiński’s rank for groups and semigroups

Identyfikatory
Warianty tytułu
Konferencja
6th European Congress of Mathematics, 2-7 July 2012 Kraków
Języki publikacji
EN
Abstrakty
Rocznik
Strony
209--215
Opis fizyczny
Bibliogr. 37 poz., rys.
Twórcy
  • Mathematical Institute, University of St Andrews North Haugh, St Andrews, Fife, KY16 9SS, Scotland
autor
  • Mathematical Institute, University of St Andrews North Haugh, St Andrews, Fife, KY16 9SS, Scotland
Bibliografia
  • [1] J. Araujo, J. D. Mitchell, N. Silva, On generating countable sets of endomorphisms, Algebra Universalis 50 (2003), 61-67.
  • [2] S. Banach, Sur un theorème de W. Sierpiński, Fund. Math. 25 (1935), 5-6.
  • [3] G. M. Bergman, Generating infinite symmetric group, Bull. London Math. Soc. 38 (2006), 429-440.
  • [4] D. Calegari, M. H. Freedman, Distortion in transformation groups, Geom. Topol. 10 (2006), 267-293.
  • [5] P. J. Cameron, Permutation groups, London Mathematical Society Student Texts, vol. 45, Cambridge University Press, Cambridge 1999.
  • [6] H. Cook, W.T. Ingram, Obtaining AR-like continua as inverse limits with only two bonding maps, Glasnik Mat. Ser. Ill 4 (1969), 309-312.
  • [7] I. Dolinka, The Bergman property for endomorphism monoids of some Fraїssé limits, Forum Mathematicum (2011), to appear, available at arXiv: 1009.2106v3.
  • [8] R. Dougherty, J. Mycielski, Representations of infinite permutations by words II, Proc. Amer. Math. Soc. 127 (1999), 2233-2243.
  • [9] M. Droste, J. K. Truss, On representing words in the automorphism group of the random graph, J. Group Theory 9 (2006), 815-836.
  • [10] M, Droste, R Göbel. On the homeomorphism groups of Cantor’s discontinuum and the spaces of rational and irrational numbers, Bull. London Math Soc. 34. (2002), 474-478.
  • [11] J. East, Generation of infinite factorizable inverse monoids, Semigroup Forum (2011).
  • [12] A. Ehrenfeucht, D. M. Silberger, Universal terms of the form BnAm, Algebra Universalis 10 (1980), 96-116.
  • [13] T. Evans, Embedding theorems for multiplicative systems and projective geometries, Proc. Amer. Math. Soc. 3 (1952), 614-620.
  • [14] F. Galvin, Generating countable sets of permutations, J. London Math. Soc. 51 (1995). 230-242.
  • [15] P. M. Higgins, J. M. Howie, J. D. Mitchell, N. Ruškuc, Countable versus uncountable ranks in infinite semigroups of transformations and relations, Proc. Edinb. Math. Soc. 46 (2003), 531-544.
  • [16] G. Higman, B. H. Neumann, H. Neumann, Embedding theorems for groups, J. London Math. Soc. 24 (1949), 247-254.
  • [17] V. Jarnik, V. Knichal, Sur l’approximation des fonctiones continues par les superpositions de deux fonctions, Fund. Math. 24 (1935), 206-208.
  • [18] A. S. Kechris, V. G. Pestov, S. Todorcevic, Ramsey theory, and topological dynamics of Fraїssé limits, automorphism groups, Geom. Funct. Anal. 15 (2005), 106-189.
  • [19] A. Khelif, A propos de la propriete de Bergman, C. R. Math. Acad. Sci. Paris 342 (2006), 377-380.
  • [20] R. C. Lyndon, Words and infinite permutations, Mots, Lang. Raison. Calc. (Hermes, Paris) (1990), 143-152.
  • [21] K. D. Magill, Universal algebra and applications, Banach Center Publ., vol. 9, PWN, Warsaw 1978.
  • [22] K. D. Magill, The countability index of the endomorphism semigroup of a vector space, Linear and Multilinear Algebra 22 (1988), 349-360.
  • [23] K. D. Magill Jr, S. Subbiah, Finitely generated dense subsemigroups of S(X), Questions Answers Gen. Topology 1 (1983), 77-87.
  • [24] V. Maltcev, J. D. Mitchell, N. Ruškuc, The Bergman property for semigroups, J. London Math. Soc. 80 (2009), 212-232.
  • [25] Z. Mesyan, Endomorphism rings generated using small numbers of elements, Bull. London Math. Soc 39 (2007), 290-300.
  • [26] J.D. Mitchell, Y. Peresse, Generating countable sets of surjective functions, Fund. Math. 213 (2011), 67-93.
  • [27] J. D. Mitchell, Y. Peresse, M.R. Quick, Generating sequences of functions, Q. J. Math 58 (2007), 71-79.
  • [28] J. Mycielski, Representations of infinite permutations by words, Proc. Amer. Math. Soc. 100 (1987), 237-241.
  • [29] J. Myhill, A. Adler, Problems and Solutions: Solutions of Advanced Problems: 6244, Amer. Math. Monthly 87 (1980), 676-678.
  • [30] K. C. O’Meara, Embedding countable rings in 2-generator rings, Proc. Amer. Math. Soc. 100 (1987), 21-24.
  • [31] O. Ore, Some remarks on commutators, Proc. Amer. Math. Soc. 2 (1951), 307-314.
  • [32] Y. Peresse, Generating uncountable transformation semigroups, PhD thesis, University of St Andrews, Scotland, August 2009.
  • [33] J. Schreier, S. Ulam, Über topologische Abbildungen der euklidischen Sphdren, Fund. Math. 23 (1934), 102-118.
  • [34] W. Sierpiński, Sur l’approximation des fonctions continues par les superpositions de quatre fonction, Fund. Math. 23 (1934), 119-120.
  • [35] W. Sierpiński, Sur les suites infinies de fonctions définies dans les ensembles quel-conques, Fund. Math. 24 (1935), 209-212.
  • [36] S. Subbiah, A dense subsemigroup of S(R) generated by two elements, Fund. Math. 117 (1983), 85-90.
  • [37] S. Subbiah, Some finitely generated subsemigroups of S(X), Fund. Math. 86 (1975), 221-231.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-d992e2e5-d15f-458a-8098-c1b4df4acbda
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