marcusc31415 / localactiondiagrams

The GAP package LocalActionDiagrams

This package implements a category for Local Action Diagrams, which were first introduced by C. Reid and S. Smith in [1]. To install it, placed it in the pkg folder of a GAP root directories. GAP root directories can be found from the GAPInfo.RootPaths variable in a GAP session.

To load the package in GAP, use LoadPackage("localactiondiagrams"). Note that this package requires the Digraphs package.

To make a local action diagram in GAP, use the LocalActionDiagramFromData(D, vl, el, r) function, where D is an immutable digraph, vl is a list of groups labelling the vertices of D, el is a list of sets labelling the edges of D, and r is a reversal mapping of the edges of D. The LocalActionDiagramFromData function will check that the data forms a valid local action diagram while the LocalActionDiagramFromDataNC won't.

Currently the package supports finding local action diagrams isomorphisms through the IsomorphismLocalActionDiagrams function, finding strongly confluent partial orientations through the LocalActionDiagramScopos function, and enumerating all local action diagrams with one or two vertices with labels that are subgroups of Aut(T_d) with the AllLocalActionDiagrams function.

References

[1] C. D. Reid and S. M. Smith, Groups acting on trees with tits’ independence property (p), 2020. DOI:10.48550/ARXIV.2002.11766. [Online]. Available:c https://arxiv.org/abs/2002.1176