Reading Question 6.1.1. Let G be a group. Which of the following claims is true? Select all that apply. (a) If G has an element of order |G|, then G is cyclic. (b) If G is cyclic, then G is abelian. (c) If G is cyclic, then G has an element of order |G|. (d) If G is abelian, then G is cyclic.

3.11 Let (G,) be a group such that x²-e for all x E G. Show that (G,.) is abelian. (Here x2 means xx.)

Reading Question 6.2.1. Let G be a cyclic group of order 20. Which of the following claims is true? Select all that apply. (a) G has 5 elements of order 4. (b) G has 4 elements of order 5. (c) G has 1 element of order 2. (d) G contains 10 generators. (e) If a is a generator of G, then the order of ak is equal to the gcd(20, k).

Which of the following groups are isomorphic? i) Z/75Z ii) Z/3Z e Z/25Z iii) Z/15Z e Z/5Z iv) Z/3Z e Z/5Z OZ/5Z.