Depth-first Search (DFS)

[FriedrichRober]

The current methods use a Breadth-first Search (BFS) method for going through the lattice of normal subgroups. For some applications, like finding a normal subgroup of a specific index, we should be a lot faster and get to a much higher index with using DFS.

Things to note:

• We need to keep track of which quotients we have searched for, T- and P-Quotients alike.
• We need to take intersections with all groups in each step, not just the ones at higher levels.

[FriedrichRober]

We should add an option, that can select the next subgroup to consider (This way, we could also implement DFS).

For example, if we search for a subgroup of index 15, it might be usefull to first try to find a subgroup of index 3 under G, and next one of index 5 under G. Then the intersection will have index 15.

Otherwise DFS will first compute all subgroups of index 3, before finding the one of 5 under G.