6.11. (a) Prove that G acts transitively on X if and only if there is at least one x Є X such that X. (See Definition 6.20 for the definition of a transitive action.) Gx (b) Prove that G acts transitively on X if and only if for every pair of elements x, y = X there exists a group element g E G such that gx = y. (c) If G acts transitively on X, prove that #X divides #G.

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Q: Exercise 6.3.12. Suppose G is a group, a, b e G such that gcd(la\, [b|) = 1. Prove (a) n (b) = {e}.

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