Group Fixed Point

The set of points of X fixed by a group action are called the group's set of fixed points, defined by

 {x:gx=x for all g in G}.

In some cases, there may not be a group action, but a single operator T. Then {x:x in X,Tx=x} still makes sense even when T is not invertible (as is the case in a group action).

See also

Group, Group Action, Map Fixed Point

This entry contributed by Todd Rowland

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Cite this as:

Rowland, Todd. "Group Fixed Point." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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