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Thus S is a set of non-generators iffor all subsets X ⊆ G.G = 〈X, S〉 implies G = 〈X〉Lemma 7.21 The Frattini subgroup Φ(G) is a set of non-generators for afinite group G.Proof: Let G = 〈X, Φ(G)〉. If 〈X〉 ≠ G, then there exists a maximalsubgroup M of G such that 〈X〉 M