Category:Definitions/Symmetric Groups

From ProofWiki
Jump to navigation Jump to search

This category contains definitions related to Symmetric Groups.
Related results can be found in Category:Symmetric Groups.


Let $S$ be a set.

Let $\map \Gamma S$ denote the set of permutations on $S$.

Let $\struct {\map \Gamma S, \circ}$ be the algebraic structure such that $\circ$ denotes the composition of mappings.


Then $\struct {\map \Gamma S, \circ}$ is called the symmetric group on $S$.


If $S$ has $n$ elements, then $\struct {\map \Gamma S, \circ}$ is often denoted $S_n$.