The Mathematical Intelligencer

, Volume 30, Issue 2, pp 6–15

Counting Groups: Gnus, Moas, and other Exotica

  • John H. Conway
  • Heiko Dietrich
  • Eamonn A. O’Brien
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Hans Ulrich Besche and Bettina Eick, “Construction of finite groups”,J. Symbolic Comput, 27 (1999), 387–404.CrossRefMATHMathSciNetGoogle Scholar
  2. [2]
    Hans Ulrich Besche, Bettina Eick, and E. A. O’Brien, “A millennium project: constructing small groups,”Internal J. Algebra Comput., 12 (2002), 623–644.CrossRefMATHMathSciNetGoogle Scholar
  3. [3]
    Simon R. Blackburn, Peter M. Neumann, and Geetha Venkataraman,Enumeration of Finite Groups, Cambridge University Press, 2007.Google Scholar
  4. [4]
    A. Cayley, “On the theory of groups, as depending on the symbolic equation 0n = 1,”Philos. Mag. (4), 7 (1854), 40–47.Google Scholar
  5. [5]
    Heiko Dietrich and Bettina Eick, “Groups of cubefree order,”J. Algebra, 292 (2005), 122–137.CrossRefMATHMathSciNetGoogle Scholar
  6. [6]
    R. Keith Dennis, “The number of groups of order n,” in preparation.Google Scholar
  7. [7]
    Bettina Eick and E. A. O’Brien, “Enumerating pρ-groups,”J. Austral. Math. Soc. Ser. A, 67 (1999), 191–205.CrossRefMATHMathSciNetGoogle Scholar
  8. [8]
    The GAP Group, GAP—Groups, Algorithms, and Programming, Version 4.4.10; 2007. (http://www.gap-system.org).Google Scholar
  9. [9]
    G. H. Hardy and E. M. Wright,An Introduction to the Theory of Numbers. Fourth edition. Oxford University Press, Oxford, 1963.Google Scholar
  10. [10]
    Graham Higman, “Enumerating ρ-groups. I: inequalities,”Proc. London Math. Soc. (3), 10 (1960), 24–30.CrossRefMATHMathSciNetGoogle Scholar
  11. [11]
    Otto Hölder, “Die Gruppen der Ordnungenp 3, pq2, pqr, p4,”Math. Ann., 43 (1893), 301–412.CrossRefMATHMathSciNetGoogle Scholar
  12. [12]
    M. Ram Murty and V. Kumar Murty, “On groups of square-free order,”Math. Ann. 267 (1984), 299–309.CrossRefMATHMathSciNetGoogle Scholar
  13. [13]
    P. Erdős, M. Ram Murty, and M. V. Murty, “On the enumeration of finite groups,”J. Number Theory 25 (1987), 360–378.CrossRefMathSciNetGoogle Scholar
  14. [14]
    M. F. Newman, E. A. O’Brien, and M. R. Vaughan-Lee, “Groups and nilpotent Lie rings whose order is the sixth power of a prime,”J. Algebra, 278 (2004), 383–401.CrossRefMATHMathSciNetGoogle Scholar
  15. [15]
    E. A. O’Brien and M. R. Vaughan-Lee, “The groups of orderp 7 for odd primep,”J. Algebra 292 (2005), 243–258.CrossRefMATHMathSciNetGoogle Scholar
  16. [16]
    L. Pyber, “Enumerating finite groups of given order.”Ann. of Math. (2) 137 (1993), 203–220.CrossRefMATHMathSciNetGoogle Scholar
  17. [17]
    Charles C. Sims, “Enumeratingp-groups,”Proc. London Math. Soc. (3), 15 (1965), 151–166.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2008

Authors and Affiliations

  • John H. Conway
    • 1
  • Heiko Dietrich
    • 2
  • Eamonn A. O’Brien
    • 3
  1. 1.Department of MathematicsPrincetonUSA
  2. 2.Institute of Computational MathematicsTechnische Universrtät BraunschweigBraunschweigGermany
  3. 3.Department of MathematicsUniversity of AucklandAucklandNew Zealand

Personalised recommendations