TOPICS
Search

Group Fixed Point


A group fixed point in a set X is fixed by every element of the acting group G. The set of these fixed points for a group action on X is

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

In some cases, there may not be a group action, but a single map T:X->X. Then {x:x in X,Tx=x} still makes sense even when T is not invertible (unlike the maps arising from a group action).


See also

Group, Group Action, Map Fixed Point

Portions of this entry contributed by Todd Rowland

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W., with contributions by Todd Rowland. "Group Fixed Point." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GroupFixedPoint.html

Subject classifications