“…Suppose now that G = S 8 , the symmetric group on eight letters, and let F be cyclic of order 8. Choose a generator c of F and define an action of F on G by the requirement that the action of c be the conjugation by the 8-cycle τ := (1,2,3,4,5,6,7,8), so that c.σ = τ στ −1 . Now, if g is the 8-cycle (1, 3, 5, 8, 2, 4, 6, 7 Suppose now that Λ [4,2] were central.…”