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
• Peter B. Kleidman, Martin W. Liebeck, The Subgroup Structure of the Finite Classical Groups
• John N. Bray, Derek F. Holt, Colva M. Roney-Dougal, The maximal subgroups of the low-dimensional finite classical groups
• Derek F. Holt, Colva M. Roney-Dougal, Constructing Maximal Subgroups of Classical Groups
• Colva M. Roney-Dougal, Maximal subgroups of finite simple groups: classifications and applications
• Derek F. Holt, Colva M. Roney-Dougal, Constructing Maximal Subgroups of Orthogonal Groups

General lecture notes on group theory and other relevant foundations

• Derek J. S. Robinson, A Course in the Theory of Groups
• Joseph J Rotman, An introduction to the theory of groups
• Larry C. Grove, Classical Groups and Geometric Algebra

Existing code

• ClassicalMaximals: existing implementation for Magma and a partial conversion to 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
  • 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)