Talk:Group action

I'm not sure about the standard terminology here:

• Is it called "faithful" or "free"?
• Is "invariant" and "stable" really the same?
• Are the sets G.x really called "traces"? --AxelBoldt

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• It's called "faithful", or "effective". ("Free" means that only the identity element has a fixed point.)
• I'm not sure about this one. I would use "invariant" for the sense you were talking about.
• The sets G.x are usually called "orbits" (as in the Orbit-Stabilizer Theorem).

--Zundark, 2001 Oct 28

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I removed the reference to permutation groups in the first paragraph since a permutation group on M is a subgroups of Sym(M), while a transformation group G on M is given by a (not necessarily injective) homomorphism G → Sym(M). So they are not the same. AxelBoldt 17:45 Oct 31, 2002 (UTC)

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There's now an overlap with orbit (mathematics).

Charles Matthews 18:52 24 Jun 2003 (UTC)