Group action - Wikipedia: "Free (or semiregular or fixed point free) if, given g, h in G, the existence of an x in X with g⋅x = h⋅x implies g = h. Equivalently: if g is a group element and there exists an x in X with g⋅x = x (that is, if g has at least one fixed point), then g is the identity. "
"fix point free" that is, the action transforms free of fixed points
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