If substantial calculations are done in a factor it might be worth still to
construct the factor group in its own representation (for example by
calling PcGroupWithPcgs on a modulo pcgs, see PcGroupWithPcgs).
The following functions are intended for working with factor groups obtained by factoring out the tail of a pcgs. They provide a way to map elements or induced pcgs quickly in the factor (respectively to take preimages) without the need to construct a homomorphism.
The setup is always a pcgs pcgs of G and a pcgs fpcgs of a factor group H = G /N which corresponds to a head of pcgs.
No tests for validity of the input are performed.
ProjectedPcElement( pcgs, fpcgs, elm ) F
returns the image in H of an element elm of G.
ProjectedInducedPcgs( pcgs, fpcgs, ipcgs ) F
ipcgs must be an induced pcgs with respect to pcgs. This operation returns an induced pcgs with respect to fpcgs consisting of the nontrivial images of ipcgs.
LiftedPcElement( pcgs, fpcgs, elm ) F
returns a preimage in G of an element elm of H.
LiftedInducedPcgs( pcgs, fpcgs, ipcgs, ker ) F
ipcgs must be an induced pcgs with respect to fpcgs. This operation returns an induced pcgs with respect to pcgs consisting of the preimages of ipcgs, appended by the elements in ker (assuming there is a bijection of pcgs mod ker to fpcgs). ker might be a simple element list.
[Top] [Previous] [Up] [Next] [Index]
GAP 4 manual