CYCLIC GROUP – NAT – LEVEL-2

Let and let |a|=12. Then, number of generators for the subgroup of G of order b are ______.

Number of elements or order 8 in are ______.

Number of elements or order 2 in D₃₃ are _______

Let be the group of rational number of under addition. Then, number of element(s) of finite order in is/are ____?

G is an abelian cyclic group and contains cyclic subgroup of orders 4 and 5. Then, other sizes of cyclic group that G must contains are 1, 2, 2n, 4n, where value of n is ____?

Let a be an element of a group and let |a| = 15. Then, order of a⁸ is _______.

The set {7, , 49, 77} forms a group under multiplication modulo 84. Then, value of is _____?

Number of cyclic subgroups of U(30) are _____

Number of subgroups of the group of integers mod 40 is ______.

Let be the group of rational number of under addition. Then, number of element(s) of finite order in is/are ____?