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If M is a proper subgroup of G we call it maximal if M≤ X ≤ G implies X = M or X = G. The Frattini subgroup of a group G is defined to be the intersection of all the maximal subgroups. (a) Prove that the Frattini subgroup Fratt (G) is characteristic in G. (b) If HG and H.Fratt (G) = G show that H = G. (Hint: If H
