The induced pcgs Q of U is called canonical if the matrix of exponent vectors contains normed vectors only and above each leading entry in the matrix there are 0's only. The canonical pcgs of U with respect to P is unique and hence such pcgs can be used to compare subgroups.
IsCanonicalPcgs( pcgs ) P
An induced pcgs is canonical if the matrix of the exponent vectors of
the elements of pcgs with respect to ParentPcgs(pcgs) is in
Hermite normal form
(see SOGOS). While a subgroup can have various
induced pcgs with respect to a parent pcgs a canonical pcgs is unique.
CanonicalPcgs( pcgs ) A
returns the canonical pcgs corresponding to the induced pcgs pcgs.
gap> G := Group((1,2,3,4),(5,6,7)); Group([ (1,2,3,4), (5,6,7) ]) gap> P := Pcgs(G); [ (5,6,7), (1,2,3,4), (1,3)(2,4) ] gap> I := InducedPcgsByPcSequence(P, [(5,6,7)*(1,3)(2,4),(1,3)(2,4)] ); [ (1,3)(2,4)(5,6,7), (1,3)(2,4) ] gap> CanonicalPcgs(I); [ (5,6,7), (1,3)(2,4) ]
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GAP 4 manual