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2 Functions

Here we include a list of all functions that are provided to the User.

2.1 Wreath Product Decomposition

The returned embeddings, i.e. wreath product decompositions, map into specialised wreath product representations, the ones obtained by WreathProduct. The main way for the User to look at a wreath product in a "human-readable" way is either by using an isomorphism from such a specialised wreath product representation to a generic representation via IsomorphismWreathProduct or by using the low-level function ListWreathProductElement.

2.1-1 WreathProductDecomposition

Let G be a group or a recog node, and optrec be an options record. Returns fail or a wreath product decomposition of G, i.e. an embedding from G to a natural wreath product, unless the debug option is set to true (see below). The following components of optrec are supported. Many more technical components are supported, however, they might be due to change during development. We therefore refer advanced users to the comments in the code to see all available options. Suppose that G ≤ K ≀ H with H ≤ Sym(m).

action

"product action" for permutation group, assume product action

"imprimitive action" for permutation or matrix group, assume imprimitive action

fail no assumptions DEFAULT

assumeSimpleBaseComponent

true assume K is non-abelian simple DEFAULT

false no assumptions

debug

true return record containing "res", "data" and "options":

• "res" is true if embedding was computed, otherwise fail

• "data" is record containing all intermediate results of the computation

• "options" is a copy of the used options record in the computation

false return fail or embedding DEFAULT

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