# Normal subgroups of the fundamental group of a non-orientable surface.

Let $N^2_g$ be a non-orientable closed genus $g\geq 2$ surface. Is there a way to explicitly list the normal subgroups of $\pi_1(N^2_g)$ in terms of generators and relations? I am interested in understanding all possible normal coverings of $N^2_g$.

Thank you.

• I assume that you are familiar with the fundamental group of non-orientable closed genus $g\ge 2$ surfaces $N_g^2$, namely $\pi_1(N_g^2,\ast)=\langle x_1,...,x_g|x_1^2\cdots x_g^2\rangle$. This paper tells you something about subgroups (not necessarily normal) of orientable genus $g$ surfaces. Maybe it is helpful to get a feeling for the general procedure. – Daniel Bernoulli Oct 5 '15 at 13:01
• The cardinality of the set of normal subgroups is continuum, hence, listing (in any meaningful sense) such subgroups is impossible. – Moishe Kohan Jan 3 at 13:24