# Math Help - Group theory

1. ## Group theory

Prove that $<\mathbb Q, +>$ group has no finite set of generators.

Any help would be appreciated!

2. For the ease of notation, suppose there are two generators, $m_1/n_1, m_2/n_2$. Let $p$ be a prime such that $\gcd(n_1, n_2,p)=1$. Is it possible to write $1/p$ as a combination of $m_1/n_1, m_2/n_2$?

You can generalize this argument for any supposed number of generators.