# Math Help - generator for groups.

1. ## generator for groups.

G=(Z,+)
X ={2,3}

Does X generate G???

My answer is no because X will only generate the set 2Z and 3Z but not Z...
Is this right if this is wrong please explain why???

2. Originally Posted by Dreamer78692
G=(Z,+)
X ={2,3}

Does X generate G???

My answer is no because X will only generate the set 2Z and 3Z but not Z...
Is this right if this is wrong please explain why???
No, that's not right. For example, $2+2+3=7 \not\in 2 \mathbb{Z} \cup 3 \mathbb{Z}$.

What you need to do for this question is to apply the Euclidean algorithm. 2 and 3 are coprime, so...