The symmetric group of Degree is the Group of all Permutations on
symbols. is therefore of Order and contains as Subgroups every
Group of Order . The number of Conjugacy Classes of
is given by the Partition Function *P*.

Netto's Conjecture states that the probability that two elements and of a symmetric group generate the entire group tends to 3/4 as . This was proven by Dixon in 1967.

**References**

Lomont, J. S. ``Symmetric Groups.'' Ch. 7 in *Applications of Finite Groups.* New York: Dover, pp. 258-273, 1987.

Wilson, R. A. ``ATLAS of Finite Group Representation.'' http://for.mat.bham.ac.uk/atlas/html/contents.html#alt.

© 1996-9

1999-05-26