- #1

Mr Davis 97

- 1,462

- 44

## Homework Statement

Consider G = {1, 8, 12, 14, 18, 21, 27, 31, 34, 38, 44, 47, 51, 53, 57, 64} with

the operation being multiplication mod 65. By the classification of finite abelian groups, this

is isomorphic to a direct product of cyclic groups. Which direct product?

## Homework Equations

## The Attempt at a Solution

Since this abelian group has 16 elements, up to isomorphism there are three options: ##\mathbb{Z}_2 \times \mathbb{Z}_2 \times \mathbb{Z}_2 \times \mathbb{Z}_2## or ##\mathbb{Z}_4 \times \mathbb{Z}_2 \times \mathbb{Z}_2##, or ##\mathbb{Z}_8 \times \mathbb{Z}_2##.

I am not sure how to determine which one...