[GAP Forum] StructureDescription Revisited

[Stefan Kohl]

Dear Forum,

Nilo de Roock wrote:

> I am doing some experiments regarding generating sets of matrices and
> the structure of the group they generate. I use for example the
> following function:
> 
> testG:=function(a,b)
> 	local M1;
> 	M1:=[[ [ 0, -E(a)^-1 ], [ -E(a), 0 ] ],[ [ 0, -1 ], [ 1, 0 ] ], [ [
> E(4*b), 0 ], [ 0, -E(4*b) ] ],[ [ -1, 0 ], [ 0, -1 ] ]];
> 	return (Group(M1));
> end;
> 
> I noticed the (for me...) interesting result that
> StructureDescription(testG(8,1)) = QD16
> StructureDescription(testG(8,3)) =C3 X QD16
> StructureDescription(testG(8,5))= C5 X QD16
> For other numbers however...
> StructureDescription(testG(8,2))= GAP Error*
> StructureDescription(testG(8,4))= GAP Error*
> StructureDescription(testG(8,7))=  GAP Error*
> 
> *="... Error, no method found! For debugging hints type ?Recovery from
> NoMethodFound
> Error, no 2nd choice method found for `IsNaturalGL' on 1 arguments called fro\
> m..."
> ( I interpreted the errors as "does not generate a group", or a bug in
> StructureDescription() for which a fix is due...)

Thanks for reporting this!

This problem will be fixed in the next update.

In the meantime -- as already several people have suggested --
you can use

     StructureDescription( Image ( IsomorphismPermGroup( <G> ) ) )

instead.

Technically, the reason for the error message is that a trivial method for
`IsGeneralLinearGroup' for matrix groups in lib/grpmat.gi which is ranked
higher than the nontrivial method for generic groups in lib/grpnames.gi
calls the operation `IsNaturalGL', for which currently no nontrivial method
is available.

Thanks again and best wishes,

     Stefan Kohl

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Stefan Kohl
Institut für Geometrie und Topologie
Pfaffenwaldring 57
Universität Stuttgart
70550 Stuttgart / Germany

E-mail: kohl at mathematik.uni-stuttgart.de
Web:    http://www.cip.mathematik.uni-stuttgart.de/~kohlsn/
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