A group 
acts freely on a set 
if no nonidentity element of 
fixes a point of 
. Equivalently, the isotropy
group of every point is the trivial group.
Freely
See also
Effective Action, Free Action, Group, Group Action, Group Fixed Point, Group Orbit, Group Representation, Isotropy Group, Lie Group Quotient Space, Matrix Group, Topological Group, TransitivePortions of this entry contributed by Todd Rowland
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Cite this as:
Weisstein, Eric W., with contributions by Todd Rowland. "Freely." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Freely.html