Symmetric Group
The symmetric group 
of Degree 
is the Group of all Permutations on symbols. is therefore of Order 
and contains as Subgroups everyGroup 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 theentire 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.
- Efron's Dice
- Egg
- Egyptian Fraction
- Ehrhart Polynomial
- Ei
- Eigenfunction
- Eigenvalue
- Eigenvector
- Eight Curve
- Eight-Point Circle Theorem
- Eight Surface
- Eikonal Equation
- Eilenberg-Mac Lane Space
- Eilenberg-Mac Lane-Steenrod-Milnor Axioms
- Eilenberg-Steenrod Axioms
- Ein Function
- Einstein Functions
- Einstein Summation
- Eisenstein Integer
- Eisenstein-Jacobi Integer
- Eisenstein Prime
- Eisenstein Series
- Eisenstein Unit
- Elastica
- Elation