Implement standard generators of groups S and G in cases L, S, U

[TristanPfersdorff]

Implement standard generators of groups S and G in cases L, S, U with the requirements of Theorem 3.11 in [HR10]. This is needed for future constructions in the O case. The constructions are given in [T87], which I was not able to cite very well, presumably since according to Taylor's website, it is only a technical report and not a research paper (I can't seem to find any fitting URL or doi, I also cannot find it in the library of the TU Kaiserslautern or of the University of Sydney). This report also does not seem to fit Theorem 3.11 in [HR10] perfectly, so I'm taking some creative liberties to ensure that the generators are suitable for future constructions.

Checklist for the reviewer

General

• [ ] All functions have unit tests

Functions constructing generators of maximal subgroups

• [ ] The code which computes and then stores the sizes is correct. To do this one confers to the tables referenced by the code.
• [ ] The test suite checks whether all constructed generators are sensible. That is it tests the generators'
  • [ ] determinants (and if applicable also the spinor norms are correct), and
  • [ ] compatibility with the correct form,
  • [ ] DefaultFieldOfMatrixGroup returns the correct field.

Functions assembling the list of all maximal subgroups of a certain group

• [ ] The code agrees with the tables in section 8.2 of the book "The Maximal Subgroups of the Low-dimensional Finite Classical Groups".

The reviewer doesn't need to compare our results to magma's results. That's the job of the person implementing the code.

[codecov[bot]]

Codecov Report

Merging #103 (531fb6c) into main (b6569d8) will increase coverage by 0.04%. The diff coverage is 100.00%.

@@            Coverage Diff             @@
##             main     #103      +/-   ##
==========================================
+ Coverage   95.55%   95.59%   +0.04%     
==========================================
  Files          14       14              
  Lines        3194     3227      +33     
==========================================
+ Hits         3052     3085      +33     
  Misses        142      142              

Impacted Files	Coverage Δ
gap/Utils.gi	93.81% <100.00%> (+0.55%)	:arrow_up:

[TristanPfersdorff]

On second thought, I really don't think we need to implement any of the standard generators for the S and U case. Their only special properties according to Theorem 3.11 would be that all possible entries of the matrices are known, and I really don't think we actually care about that. With that in mind, this PR is probably ready, the title is not quite apt anymore.