![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() |
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.
See also Alternating Group, Conjugacy Class, Finite Group, Netto's Conjecture, Partition Function P, Simple Group
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.