Group action Free group action A group action of on is called free or semiregular iff the Stabilizer group of every is , #m/def/group i.e. for all . Properties A free group action is necessarily effective. Proof of 1Since for all and , the induced automorphism cannot be identity for such a , hence is a group monomorphism proving ^P1. #state/tidy | #lang/en | #SemBr