Pacific Journal of Mathematics

What is the probability that two elements of a finite group commute?

David J. Rusin

Article information

Source
Pacific J. Math. Volume 82, Number 1 (1979), 237-247.

Dates
First available: 8 December 2004

Permanent link to this document
http://projecteuclid.org/euclid.pjm/1102785075

Zentralblatt MATH identifier
0408.20058

Zentralblatt MATH identifier
0398.20089

Mathematical Reviews number (MathSciNet)
MR549847

Subjects
Primary: 20D99: None of the above, but in this section

Citation

Rusin, David J. What is the probability that two elements of a finite group commute?. Pacific Journal of Mathematics 82 (1979), no. 1, 237--247. http://projecteuclid.org/euclid.pjm/1102785075.


Export citation

References

  • [1] E. A. Bertram, A density theorem on the numberof eonjugacy classes infinite groups, Pacific J. Math., 55 (1974), 329-333.
  • [2] P. Erds and P. Turan, On some problems of a statistical group theory, IV, Acta Math. Acad. Sci. Hung., 19 (1968), 413-435.
  • [3] W. Feit and N. J. Fine, Pairs of commuting matrices over a finite field, Duke Math. J., 27 (1960), 91-94.
  • [4] W. H. Gustafson, What is the probability that two group elements commute*! Amer. Math. Monthly, 80 (1973), 1031-1034.
  • [5] B. Huppert, Endliche Gruppe I, Springer Verlag, Berlin, 1967.
  • [6] N. Jacobson, Basic Algebra I, W. H. Freeman and Co., San Francisco, (1974), 457-465.
  • [7] K. Joseph, Several conjectures on commutativityin algebraic structures,Amer. Math. Monthly, 84 (1977), 550-551.
  • [8] P. X. Gallagher, The number of eonjugacy classes in a finite group, Math. Z., 118 (1970), 175-179.
  • [9] D. MacHale, Commutativityin finite rings, Amer. Math. Monthly, 83 (1976), 30-32.
  • [10] D. MacHale, How commutative can a non-commuiativegroup be Math. Gazette, LVIII (1974), 199-202.
  • [11] I. D. MacDonald, Some explicit bounds in groups with finite derived qroups, Proc. London Math. Soc, Series 3 11 (1961), 23-56.
  • [12] M. Newman, A bound for the number of eonjugacy classes in a group, J. London Math. Soc, 43 (1960), 108-110.
  • [13] W. R. Scott, Group Theory, Prentice Hall, Englewood Cliffs (N. J.) (1964), (450).
  • [14] G. Sherman, What is the probability an automorphism fixes a group element*! Amer. Math. Monthly, 82 (1975), 261-264.
  • [15] G. Sherman, A lower bound for the number of eonjugacy classes in a finite nilpotent group, Notices Amer. Math. Soc, 25 (1978), A68.
  • [16] L. Weisner, Abstract Theory of Inversion of Finite Series, Trans. Amer. Math. Soc, 38 (1935), 474-492.