Implement IsMinimalNonmonomial for nonsolvable groups

[jackschmidt]

Resolves #4452

Description

Text for release notes

Implement IsMinimalNonmonomial for nonsolvable groups

(End of text for release notes)

Further details

The previous implementation followed van der Waall in only handling
solvable groups. Indeed in the paper,
MR507832
van der Waall says the nonsolvable groups can easily be disposed
of using Thompson's N-groups papers, however he does not state the
result.

Luckily most of the minimal simple groups are also minimal
non-monomial. The exception is just PSL(3,3) which contains a subgroup
isomorphic to the non-monomial group SL(2,3). The groups of the form
PSL(2,q) are handled by Dickson's classification of their subgroups,
all of which are metabelian or non-solvable. Since the non-solvable
subgroups are eliminated by being minimal simple, we have only
monomial subgroups. The Suzuki groups require a short argument,
given in the source. Suzuki 1960 lists the maximal subgroups, and all
but the Sylow 2-normalizer are metabelian. The Sylow 2-normalizer's
characters are described in sufficient detail in the paper to ensure
they are monomial.

Checklist for pull request reviewers

• proper formatting

If your code contains kernel C code, run clang-format on it; the
simplest way is to use git clang-format, e.g. like this (don't
forget to commit the resulting changes):

git clang-format $(git merge-base HEAD master)

• usage of relevant labels

  1. either release notes: not needed or release notes: to be added
  2. at least one of the labels bug or enhancement or new feature
  3. for changes meant to be backported to stable-4.X add the backport-to-4.X label
  4. consider adding any of the labels build system, documentation, kernel, library, tests

• runnable tests

• lines changed in commits are sufficiently covered by the tests

• adequate pull request title

• well formulated text for release notes

• relevant documentation updates

• sensible comments in the code

[fingolfin]

Thank you very much for this very nice contribution! I left some remarks, and I think one case needs to be added.

[wilfwilson]

Thank you for this, especially the very helpful comments. I spotted just a couple of typos in them.

[fingolfin]

I've applied the corrections by @wilfwilson and squashed the four commits into one. If the tests pass, let's merge it. Thanks again, @jackschmidt !