MTX.InducedActionSubmodule(module,sub) F
MTX.InducedActionSubmoduleNB(module,sub) F
creates a new module corresponding to the action of module on sub. In
the NB version the basis sub must be normed. (That is it must be in
echelon form with pivots normed to 1.)
MTX.InducedActionFactorModule(module,sub[,compl]) F
creates a new module corresponding to the action of module on the factor of sub. If compl is given, it has to be a basis of a (vectorspace-)complement of sub. The action then will correspond to compl.
MTX.InducedAction(module,sub[,type]) F
Computes induced actions on submodules or factormodules and also returns the corresponding bases. The action taken is binary encoded in type: 1 stands for subspace action, 2 for factor action and 4 for action of the full module on a subspace adapted basis. The routine returns the computed results in a list in sequence (sub,quot,both,basis) where basis is a basis for the whole space, extending sub. (Actions which are not computed are omitted, so the returned list may be shorter.) If no type is given, it is assumed to be 7. The basis given in sub must be normed!
All these routines return fail if sub is not a proper subspace.
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GAP 4 manual