Question

The generators of the set of integers $\mathbb{Z}$ under addition is:

• A. Only 1.
• B. Only $-1$.
• C. Both 1 and $-1$.
• D. 1, 2 and $-1$.

Hint:

An infinite cyclic group is always isomorphic to $(\mathbb{Z}, +)$ and possesses exactly 2 generators ($g$ and $g^{-1}$). A finite cyclic group $\mathbb{Z}_n$ has $\phi(n)$ generators, where $\phi$ is Euler's totient function.

Answer 1

The Correct Option is C