The orbit of s is the set G⋅s={g⋅s∣g∈G}, the full set of objects that s is sent to under the action of G. The first condition for a group action holds by associat...The orbit of s is the set G⋅s={g⋅s∣g∈G}, the full set of objects that s is sent to under the action of G. The first condition for a group action holds by associativity of the group, and the second condition follows from the definition of the identity element. (There is also a right regular action, where g⋅h=hg; the action is 'on the right'.) The Cayley graph of the left regular action is the same as the usual Cayley graph of the group!
