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Is there a name for a set together with a unary operation?

If so, where can I learn more about them? Is there anything interesting about them? Are they simply a special case of groups? It simply occurred to me and Googling around has failed me.

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It is called a function from the set to itself.... – N. S. Apr 1 '12 at 0:17
You might also be interested in involutions. They tend to appear in all sorts of algebraic situations. See also here. – Dejan Govc Apr 1 '12 at 0:21
From Wikipedia/Outline of algebraic structures#Simple structures: "Unary system: S and a single unary operation over S." – user2468 Apr 1 '12 at 1:24
I think some people define discrete dynamical systems that way. – Michael Greinecker Apr 1 '12 at 2:20

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