13. U(5) Z4 True ● False 14. A subgroup of a group is a left coset of itself. True False ●
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- 10.3.3. Let G = Z/4Z × Z/6Z, and let H be the subgroup of G generated by (2,2). (a) What are the elements of H? (b) What are the elements of G/H? (c) Find a familiar group that is isomorphic to G/H.(d) Find the cosets of the quotient group (5)/(10), and determine its order.Q 5 Find the inverse of the element 9 in the group (U(10), ®10). Q 6 Find the order of the element 2 in the group (Zs, s). Q 7 Find the generators of the group (Z9, ®9). Q 8 List all the subgroups of the group (Z4, ®4).
- (C203, x) is a Sub group of ( (l{0}, ^) - Fill in Ihe blanke box in the group. H={1,-1, i, - i} is a cglby fable belo. -1 -- -1 %3B7. [10] Let G be a group, with x E G and o (x) = 48. Give the order of the following elements of G: a) o(x²) b) o (x20) c) o(x23)46. Determine whether (Z, - {0}, 6 ) is it a group or not? Explain your answer?