# Gracious Living

Symmetric Groups
December 18, 2010, 11:36
Filed under: Algebra, Math, Uncategorized | Tags: , , , ,

We’ve seen symmetric groups before.  The symmetric group on an arbitrary set, $S_X$ or ${\rm Sym}(X)$, is the group of bijections from the set to itself.  As usual, we’re only interested in the finite case $S_n$, which we call the symmetric group on $n$ symbols.  These are pretty important finite groups, and so I hope you’ll accept my apology for writing a post just about their internal structure.  The language we use to talk about symmetric groups ends up popping up all the time.