The Mathematical Intelligencer

, Volume 14, Issue 3, pp 54–57 | Cite as

The Ubiquity of Free Groups

  • A. M. W. Glass
Article

Keywords

Free Group Automorphism Group Free Product Galois Theory Free Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    S. A. Adeleke, A. M. W. Glass, and L. Morley, Arithmetic permutations,J. London Math. Soc. (to appear).Google Scholar
  2. 2.
    S. D. Cohen, The group of translations and rational powers is free, (submitted).Google Scholar
  3. 3.
    J. D. Dixon, Most finitely generated permutation groups are free,Bull. London Math. Soc. 22 (1990), 222–226.CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    M. Droste, Structure of partially ordered sets with transitive automorphism groups,Mem. Amer. Math. Soc. 334 (1985).Google Scholar
  5. 5.
    D. B. A. Epstein, Almost all subgroups of a Lie group are free,J. Algebra 19 (1971), 261–262.CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    A. M. W. Glass and S. H. McCleary, Highly transitive representations of free groups and free products,Bull. Austral. Math. Soc. 43 (1991), 19–36.CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    A. M. W. Glass, S. H. McCleary, and M. Rubin, The automorphism group of the countable universal poset (submitted).Google Scholar
  8. 8.
    S. V. Gunhouse, Highly transitive representations of free products on the natural numbers,Arch. Math. (to appear).Google Scholar
  9. 9.
    K. K. Hickin, Highly transitive Jordan representations of free products,J. London Math. Soc. (to appear).Google Scholar
  10. 10.
    D. L. Johnson, The group of formal power series under substitution,J. Austral. Math. Soc. (Series A) 45 (1988), 296–302.CrossRefMATHGoogle Scholar
  11. 11.
    A. Karrass and D. Solitar, Some remarks on the infinite symmetric group,Math. Z. 66 (1956), 64–69.CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    H. D. Macpherson, Groups of automorphisms of ℵ0- categorical structures,Quart. J. Math. Oxford (2) 37 (1986), 449–465.CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    T. P. McDonough, A permutation representation of a free group,Quart. J. Math. Oxford (2)28 (1977), 353–356.CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    J. F. Ritt, Prime and compositive polynomials,Trans. Amer. Math. Soc. 23 (1922), 51–66.CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    J. Tits, Free subgroups in linear groups.J. Algebra 20 (1972), 250–270.CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    J. K. Truss, The group of the countable universal graph,Math. Proc. Cambridge Phil. Soc. 98 (1985), 213–245.CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    S. White, The group generated byx→x + 1 andx→x p is free,J. Algebra 118 (1988), 408–422.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Verlag 1992

Authors and Affiliations

  • A. M. W. Glass
    • 1
  1. 1.Department of Mathematics and StatisticsBowling Green State UniversityBowling GreenUSA

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