Explore group actions, which are ways in which groups act on sets, and examine the properties and applications of group actions in various mathematical contexts.
Group Actions Definition A group action is a way a group G "acts" on a set X, formally a function G x X -> X satisfying ex = x and (gh)x = g(hx) for all g, h in G, x in X. Orbit The orbit of an element x is the set of all elements it can be mapped to by applying every element of G. Stabilizer The stabilizer of x is the subgroup of elements in G that leave x unchanged (fix x...…
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