Question

give an example of a finite abelian gruop which is not cyclic​

Answer 1

Answer:

Consider Z1+Z2+Z3. It clearly has 2⋅2⋅3=122⋅2⋅3=12 elements, but every element has order dividing 66, so there cannot be an element of order 1212, so it isn't cycle

Answer 2

Answer:

Consider Z1+Z2+Z3. It clearly has 2⋅2⋅3=122⋅2⋅3=12 elements, but every element has order dividing 66, so there cannot be an element of order 1212, so it isn't cyclic.