symmetric group

Let $X$ be a set. Let $S(X)$ be the set of permutations of $X$ (i.e. the set of bijective functions on $X$). Then the act of taking the composition of two permutations induces a group structure on $S(X)$. We call this group the symmetric group and it is often denoted $\mathrm{Sym}(X)$.

When $X$ has a finite number $n$ of elements, we often refer to the symmetric group as $S_n$, and describe the elements by using cycle notation.

Title	symmetric group
Canonical name	SymmetricGroup1
Date of creation	2013-03-22 14:03:53
Last modified on	2013-03-22 14:03:53
Owner	antizeus (11)
Last modified by	antizeus (11)
Numerical id	5
Author	antizeus (11)
Entry type	Definition
Classification	msc 20B30
Related topic	Symmetry2