for those partice could you help me

Does there exist an element of order 42 in A13? Justify your answer Let G be a group, a, be G and |a| = 20, |b| = 18 and (a) n (b) # {e}. Prove that a10 = 69. Let H c (Q, +) be a subgroup generated by finitely many elements. Prove that H is cyclic. Does there exist an element o E Sis such that of = (3256)? Justify your answer. Let 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0 = 12 5 6 15 1 10 20 2 13 14 17 19 18 3 9 4 7 11 8 16 (a) Find lol; (b) Is a even or odd