# Math Help - Question in group theory.

1. ## Question in group theory.

Hi all,
A student I'm helping gave me a question.

Q: Give an example of a group G with a normal subgroup N such that N and G/N are abelian, but G is not abelian.

I'm fairly sure there is a dihedral group with this property but i don't have time to find an explicit example.

Side note: If we weaken the conditions slightly and replace abelian by solvable no example exists.

2. Originally Posted by whipflip15
Hi all,
A student I'm helping gave me a question.

Q: Give an example of a group G with a normal subgroup N such that N and G/N are abelian, but G is not abelian.

I'm fairly sure there is a dihedral group with this property but i don't have time to find an explicit example.

every dihedral group $D_n, \ n \geq 3,$ satisfies the condition. because $D_n=,$ and so you just choose $N=.$