The GAP package ClassicalMaximals

Translation of magma ClassicalMaximals to GAP. For resources see this hack.md.

Status

Implementation status

Geometric maximal subgroups (Aschbacher Classes C1-C8)

• Type L: Complete for dimensions 2-12
• Type U: Complete for dimensions 3-12
• Type S: Complete for dimensions 4-12
• Type O: Complete for dimensions 3-12
  • C2 & C4: Complete for all dimensions

Almost simple groups (Class S)

• Complete for types L, U, S, O in dimensions up to 12
• Supported options (via option records, undocumented):
  • all: Conjugacy classes under the full automorphism group of the simple classical group
  • novelties: Intersections of novelty maximal subgroups with the quasisimple group
  • special: Normalisers in SO(n,q)
  • general: Normalisers in GL(n,q), GU(n,q), or GO(n,q)
  • normaliser: Normalisers in the full conformal group (preserving form modulo scalars)
    • forms preserved up to scalars are not stored (awaiting full GAP support for conformal groups)
  • all these options complete for dimensions up to 12
  • … but group sizes for special, general, normaliser are not precomputed and stored

Testing & verification

• Verification of stored bilinear/sesquilinear/quadratic forms
• Group size checks via the recog package
• Cross-checks against tables in [BHR13] for the number of maximal subgroups
  • Class S & orthogonal geometric subgroups: Tests also against Magma’s ClassicalMaximals

Roadmap / TODO

Geometric maximal subgroups (Aschbacher Classes C1-C8)

• Generalize other Aschbacher classes to work for all dimensions
• Implement all, novelties, special, general, normaliser for all geometric classes

Almost simple groups (Class S)

• Extend implementation beyond dimension 12 (for comparison: Magma covers dimensions up to 17)
• Precompute group sizes for special, general, normaliser options
• Streamline repetitive construction logic (especially in ClassicalMaximals.gi)

General features

• Adapt ConjugateToStandardForm to support forms preserved up to a scalar (depending on future updates in the forms package)

Contact

To report issues please use our issue tracker.

License

ClassicalMaximals is free software; you can redistribute and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your opinion) any later version. For more information see the LICENSE file.

Funding

The development of this GAP package is supported by the German Research Foundation (DFG) within the Collaborative Research Center TRR 195.