For in , the vertex group consists of those with , which is just the isotropy subgroup at for the given action (which is why vertex groups are also called isotropy groups). Similarly, the orbits of the action groupoid are the orbit of the group action, and the groupoid is transitive if and only if the group action is transitive.
For in , the vertex group consis,ts of those with , which is just the isotropy subgroup at for the given action (which is why vertex groups are also called isotropy groups). Similarly the orbits of the action groupoid are the orbit of the group action, and the groupoid is transitive if and only if the group action is transitive.