Abelian Quotient group, which is not normal

Question

What would be an example of a group $G$ with subgroup $H$ such that $G/H$ is abelian but $H$ is not normal?

See also http://math.stackexchange.com/questions/14282/why-do-we-define-quotient-groups-for-normal-subgroups-only/ — Tobias Kildetoft, Mar 10 '15 at 12:29

score 4 · Answer 1 · answered Mar 10 '15 at 11:50

4

You can only make quotient groups with normal subgroups. Otherwise it is not well-defined.

So it is in fact impossible to give an example of this :)

answered Mar 10 '15 at 11:50

William Kurdahl

1

It's impossible even if OP replaces "is abelian" with "exists". – Gerry Myerson Mar 10 '15 at 12:00

1 Answers1