Dear Avital and dear gap-forum,
Let G be H x K. Then the self-normalized subgroups of G should be the
subgroups S such that the projections of S onto H and K are
self-normalized in H and K respectively.
Let S be a self-normalized subgroup generated by h_1 x k_1, ...,
h_n x k_n. Then the projection of S onto H is the subgroup S_H of H
generated by h_1, ..., h_n and S_H self-normalized, this can be proved
using (h_i x k_1) ^ (h x k) = (h_i ^ h) x (k_i ^ k) .
The same for the analogous subgroup of K.