make isomorphism(PcGroup, A) for infinite abelian A work
#4319
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The documentation claimed that this is not supported, but in fact GAP's pcp groups can deal with this case. The code looks horrible, due to the fact that GAP supports the decomposition of elements in abelian groups w.r.t. independent generators only for special such generating sets. (This happens for abelian permutation groups.) Note that this is generic code. Perhaps we should add special methods for the case that we ask for a `FPGroup` or a `PcGroup`, then also the functions for computing (pre)images can be more efficient.
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Additional details and impacted files@@ Coverage Diff @@
## master #4319 +/- ##
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Coverage 84.49% 84.49%
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+ Hits 72321 72325 +4
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fingolfin
reviewed
Nov 15, 2024
| if 0 in exponents | ||
| GapG = GAP.Globals.AbelianPcpGroup(length(exponents), GapObj(exponents; recursive = true)) | ||
| G = PcGroup(GapG) |
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For Pcp groups the given exponents actually do correspond 1-1 to the given exponent vector.
On the other hand IndependentGeneratorsOfAbelianGroup output looks horrible:
gap> G:=AbelianPcpGroup([3,0,3,9,15]);
Pcp-group with orders [ 3, 0, 3, 9, 15 ]
gap> gens:=GeneratorsOfGroup(G);
[ g1, g2, g3, g4, g5 ]
gap> List(gens, Order);
[ 3, infinity, 3, 9, 15 ]
gap> IndependentGeneratorsOfAbelianGroup(G);
[ g2*g3^2*g4, g1, g3*g5^5, g4^6*g5^10, g5^6, g4^5*g5^10 ]So I think we should avoid IndependentGeneratorsOfAbelianGroup and IndependentGeneratorExponents for pcp groups.
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That is what I meant when I wrote that special methods for FPGroup and PcGroup would make sense.
fingolfin
approved these changes
Nov 15, 2024
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The documentation claimed that this is not supported, but in fact GAP's pcp groups can deal with this case.
The code looks horrible,
due to the fact that GAP supports the decomposition of elements in abelian groups w.r.t. independent generators only for special such generating sets.
(This happens for abelian permutation groups.)
Note that this is generic code.
Perhaps we should add special methods for the case that we ask for a
FPGroupor aPcGroup, then also the functions for computing (pre)images can be more efficient.resolves #4318