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: [EMAIL PROTECTED]
Web: http://www.cip.mathematik.uni-stuttgart.de/~kohlsn/
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