Dense free subgroups of automorphism groups of homogeneous partially ordered sets
-
Szymon Głab
,
Przemysław Gordinowicz
and
Filip Strobin
Abstract
A countable poset is ultrahomogeneous if every isomorphism between its finite subposets can be extended to an automorphism. If A is such a poset, then the group
References
[1] U. B. Darji and J. D. Mitchell, Highly transitive subgroups of the symmetric group on the natural numbers, Colloq. Math. 112 (2008), no. 1, 163–173. 10.4064/cm112-1-9Search in Google Scholar
[2] U. B. Darji and J. D. Mitchell, Approximation of automorphisms of the rationals and the random graph, J. Group Theory 14 (2011), no. 3, 361–388. 10.1515/jgt.2010.057Search in Google Scholar
[3] S. Gao, Invariant Descriptive Set Theory, Pure Appl. Math. 293, CRC Press, Boca Raton, 2009. 10.1201/9781584887942Search in Google Scholar
[4] P. M. Gartside and R. W. Knight, Ubiquity of free subgroups, Bull. Lond. Math. Soc. 35 (2003), no. 5, 624–634. 10.1112/S0024609303002194Search in Google Scholar
[5] E. Glasner and B. Weiss, Topological groups with Rokhlin properties, Colloq. Math. 110 (2008), no. 1, 51–80. 10.4064/cm110-1-2Search in Google Scholar
[6] A. M. W. Glass, S. H. McCleary and M. Rubin, Automorphism groups of countable highly homogeneous partially ordered sets, Math. Z. 214 (1993), no. 1, 55–66. 10.1007/BF02572390Search in Google Scholar
[7] J. Jonušas and J. Mitchell, Topological 2-generation of automorphism groups of countable ultrahomogeneous graphs, Forum Math. 29 (2017), no. 4, 905–939. 10.1515/forum-2016-0056Search in Google Scholar
[8] A. S. Kechris, Classical Descriptive Set Theory, Grad. Texts in Math. 156, Springer, New York, 1995. 10.1007/978-1-4612-4190-4Search in Google Scholar
[9] A. S. Kechris and C. Rosendal, Turbulence, amalgamation, and generic automorphisms of homogeneous structures, Proc. Lond. Math. Soc. (3) 94 (2007), no. 2, 302–350. 10.1112/plms/pdl007Search in Google Scholar
[10] D. Kuske and J. K. Truss, Generic automorphisms of the universal partial order, Proc. Amer. Math. Soc. 129 (2001), no. 7, 1939–1948. 10.1090/S0002-9939-00-05778-6Search in Google Scholar
[11] A. H. Lachlan and R. E. Woodrow, Countable ultrahomogeneous undirected graphs, Trans. Amer. Math. Soc. 262 (1980), no. 1, 51–94. 10.1090/S0002-9947-1980-0583847-2Search in Google Scholar
[12] T. P. McDonough, A permutation representation of a free group, Quart. J. Math. Oxford Ser. (2) 28 (1977), no. 111, 353–356. 10.1093/qmath/28.3.353Search in Google Scholar
[13] A. H. Mekler, Homogeneous partially ordered sets, Finite and Infinite Combinatorics in Sets and Logic (Banff 1991), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 411, Kluwer Academic, Dordrecht (1993), 279–288. 10.1007/978-94-011-2080-7_19Search in Google Scholar
[14] W. Miller, The maximum order of an element of a finite symmetric group, Amer. Math. Monthly 94 (1987), no. 6, 497–506. 10.1080/00029890.1987.12000673Search in Google Scholar
[15] J. H. Schmerl, Countable homogeneous partially ordered sets, Algebra Universalis 9 (1979), no. 3, 317–321. 10.1007/BF02488043Search in Google Scholar
[16] S. A. Solecki, Extending partial isometries, Israel J. Math. 150 (2005), 315–331. 10.1007/BF02762385Search in Google Scholar
[17] J. K. Truss, Generic automorphisms of homogeneous structures, Proc. Lond. Math. Soc. (3) 65 (1992), no. 1, 121–141. 10.1112/plms/s3-65.1.121Search in Google Scholar
[18] J. K. Truss, On notions of genericity and mutual genericity, J. Symb. Log. 72 (2007), no. 3, 755–766. 10.2178/jsl/1191333840Search in Google Scholar
© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Sharp maximal estimates for multilinear commutators of multilinear strongly singular Calderón–Zygmund operators and applications
- Infinite-dimensional triangularizable algebras
- Expansion for the product of matrices in groups
- Asphericity of positive free product length 4 relative group presentations
- Unitary representations with non-zero Dirac cohomology for complex E6
- On middle cohomology of special Artin–Schreier varieties and finite Heisenberg groups
- Normal elements of noncommutative Iwasawa algebras over SL3(ℤ_p)
- Regularity properties of Schrödinger equations in vector-valued spaces and applications
- Statistics of Hecke eigenvalues for GL(𝑛)
- Bilinear Calderón–Zygmund operators on products of variable Hardy spaces
- On the Reidemeister spectrum of an Abelian group
- Dense free subgroups of automorphism groups of homogeneous partially ordered sets
- Left semi-braces and solutions of the Yang–Baxter equation
- On the automorphism group of a symplectic half-flat 6-manifold
Articles in the same Issue
- Frontmatter
- Sharp maximal estimates for multilinear commutators of multilinear strongly singular Calderón–Zygmund operators and applications
- Infinite-dimensional triangularizable algebras
- Expansion for the product of matrices in groups
- Asphericity of positive free product length 4 relative group presentations
- Unitary representations with non-zero Dirac cohomology for complex E6
- On middle cohomology of special Artin–Schreier varieties and finite Heisenberg groups
- Normal elements of noncommutative Iwasawa algebras over SL3(ℤ_p)
- Regularity properties of Schrödinger equations in vector-valued spaces and applications
- Statistics of Hecke eigenvalues for GL(𝑛)
- Bilinear Calderón–Zygmund operators on products of variable Hardy spaces
- On the Reidemeister spectrum of an Abelian group
- Dense free subgroups of automorphism groups of homogeneous partially ordered sets
- Left semi-braces and solutions of the Yang–Baxter equation
- On the automorphism group of a symplectic half-flat 6-manifold
