###### tags: `recog`, `gap`
# Maximal subgroups of classical groups

## TODO Sergio
- Koordination Julian, Tristan, Max
- Kontakt herstellen, vielleicht einen regelmäßigen Arbeitstermin für die
drei und einen Statusupdate-Termin mit Max finden.
- Terminfinder aufsetzen, für Arbeitswoche/ARbeitstage mit allen.
- Mit Alex, Alice, Max herausfinden ob wir das als paket, in der library oder
in Julia einbinden.
- Colva und Alexander anquatschen, ob die sich mal kurz vorstellen wollen.
Darum bitten, dass sich unsere Studis bei Fragen auch an die zwei wenden
können.

## Meetings

TODO: time&dates when we meet (regularly)

### Coding Sprint

Sprints:
- Lucas: First two weeks in October?
- Anna, Daniel: August 23 - 27
- Tristan & Max: week August 30 - ..

## References

#### For maximal subgroups of classical groups
- [Nicholas Illman, *Maximal Subgroups of Classical Groups*, poster](http://www.maths.qmul.ac.uk/~mj/AnnCook/09-10/Illman.pdf)
- [Peter B. Kleidman, Martin W. Liebeck, *The Subgroup Structure of the Finite Classical Groups*](https://doi.org/10.1017/CBO9780511629235)
- [John N. Bray, Derek F. Holt, Colva M. Roney-Dougal, *The maximal subgroups of the low-dimensional finite classical groups*](https://doi.org/10.1017/CBO9781139192576)
- [Derek F. Holt, Colva M. Roney-Dougal, *Constructing Maximal Subgroups of Classical Groups*](https://doi.org/10.1112/S1461157000000899)
- [Colva M. Roney-Dougal, *Maximal subgroups of finite simple groups: classifications and applications*](https://www.cambridge.org/cz/academic/subjects/mathematics/discrete-mathematics-information-theory-and-coding/surveys-combinatorics-2021)
- [Derek F. Holt, Colva M. Roney-Dougal, *Constructing Maximal Subgroups of Orthogonal Groups*](https://doi.org/10.1112/S1461157009000035)

#### General lecture notes on group theory and other relevant foundations
- [Derek J. S. Robinson, *A Course in the Theory of Groups*](http://dx.doi.org/10.1007/978-1-4419-8594-1)
- [Joseph J Rotman, *An introduction to the theory of groups*](http://dx.doi.org/10.1007/978-1-4612-4176-8)
- [Larry C. Grove, *Classical Groups and Geometric Algebra*](http://dx.doi.org/10.1090/gsm/039)

#### Existing code

- [`ClassicalMaximals`](http://magma.maths.usyd.edu.au/magma/handbook/text/768#9097): existing implementation for [Magma](http://magma.maths.usyd.edu.au/magma/) and a partial conversion to [GAP](https://github.com/gap-system/gap): <https://github.com/hulpke/maxtrans/>
- `original` contains the unmodified Magma code
- `magma` contains slightly tweaked versions of the code to help the [Magma-to-GAP converter](https://github.com/hulpke/mgmconvert)
- `translate` contains the raw output of the Magma-to-GAP converter (this code may be wrong, even contain syntax errors)
- `final` contains manually adjusted versions of some of the automatically translated files
- the starting point for our project is `classmax.m` resp. `classmax.g` which imports code from all the other files
- in GAP, maximal subgroups can be computed via `MaximalSubgroupClassReps` resp. `ConjugacyClassesMaximalSubgroups` (the latter calls the former). But note that this mostly is generic code which does not deal specifically with matrix groups (with a few exceptions)