Gracious Living

We’ve seen symmetric groups before.  The symmetric group on an arbitrary set, or , is the group of bijections from the set to itself.  As usual, we’re only interested in the finite case , which we call the symmetric group on 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.

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