Add order_bound keyword argument to subgroup_classes

[ThomasBreuer]

No description provided.

[thofma]

Can we use inf as the default?

And can we call it order_bound? I can imagine at least two other things that one would want to bound when enumerating subgroup classes.

[thofma]

Thanks!

[fieker]

It solves my problem, but the overall strategy is wrong:

• if I given order (exactly) shouldn't this result in it being called with an order_bound and then filtered?
• if the lattice is already known, should it not be always used?

[ThomasBreuer]

• if I given order (exactly) shouldn't this result in it being called with an order_bound and then filtered?

Yes, we can use a given order also as an order_bound, that improves the case where order is given.

• if the lattice is already known, should it not be always used?

It would be tempting to say that this should be done on the GAP side.
In the current setup, this is only partially true. For the moment, this must be fixed on the Oscar side.

[fingolfin]

Do you have any test numbers to verify this is actually faster in at least some cases? Say for some small alternating or symmetric groups, and perhaps some $p$-groups or so, with order_bounds such as 5, or 50 ; compared to getting all and then filtering

[ThomasBreuer]

It seems this question becomes more involved.

• When searching for subgroups of given large exact order, using an order bound is likely not a good idea. (There is low_index_subgroup_classes for the case of very large subgroups.)
• When searching for groups of given exact order such that all groups of that order are cyclic, one should just look for elements of that order.
• When searching several times in the same group for subgroups with a given order bound or of a given order, one should probably compute all subgroup classes once, and later search in this lattice.

(It would be useful to add some remarks like that in the docstring.)

For nonsolvable groups, computing all subgroup classes seems to be quite fast, compared with computing the lattice up to a given bound.
For solvable groups, the situation looks different.

julia> @time subgroup_classes(small_group(432, 12));
  0.217451 seconds (783.03 k allocations: 48.416 MiB)

julia> @time subgroup_classes(small_group(432, 12), order_bound = 10);
  0.080356 seconds (389.78 k allocations: 24.971 MiB)

julia> @time subgroup_classes(small_group(1536, 132));
  1.962808 seconds (5.96 M allocations: 343.379 MiB)

julia> @time subgroup_classes(small_group(1536, 132), order_bound = 20);
  0.562521 seconds (2.14 M allocations: 135.414 MiB)