# Math Help - finitely generated groups

1. ## finitely generated groups

Show that if H is a normal subgroup of a group G such that H and G/H are finitely generated, then so is G

thanks!

2. Originally Posted by mms
Show that if H is a normal subgroup of a group G such that H and G/H are finitely generated, then so is G

thanks!
let $H=, \ G/H = ,$ and $g \in G.$ then $g \in H \subseteq .$ thus: $G \subseteq \subseteq G.$