Question: (a) Let G be a group. Show that every transversalT of the conjugacy classes {rG | x E G} of G contains the centre

(a) Let G be a group. Show that every transversalT of the

(a) Let G be a group. Show that every transversalT of the conjugacy classes {rG | x E G} of G contains the centre Z(G) of G. (b) Let G be a group and H a normal subgroup of finite index in G. Prove that if p is a prime number such that p | (G, H), then there exists a subgroup of G/H whose order is . (c) Let U

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