# finitely generated groups

• July 17th 2009, 03:24 PM
mms
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! (Hi)
• July 17th 2009, 04:09 PM
NonCommAlg
Quote:

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! (Hi)

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