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[Some of you may have already received this e-mail,

since it arrived just as I killed the list server. mS]

Dear Forum,

recently we had 3 different problems with GAP 3.2 which occured while

running a program written in gap's own language. The things we want

gap to compute seem to be silly, if considered isolated, but in

our program they can only be avoided with difficulties.

1. Character table of the trivial group:

gap> g:=Group(());

Group( () )

gap> CharTable(g);

Error, <G> must not be trivial in

PermGroupOps.LargestMovedPoint( G ) called from

G.operations.DxPreparation( G ) called from

DixonInit( G, opt ) called from

arg[1].operations.CharTable( arg[1] ) called from

CharTable( g ) called from

main loop

brk>

2. The command "DoubleCosets":

gap> g:=Group((1,2),(1,2,3));

Group( (1,2), (1,2,3) )

gap> h:=Subgroup(g,[(1,2)]);

Subgroup( Group( (1,2), (1,2,3) ), [ (1,2) ] )

gap> DoubleCosets(g,h,h);

Error, <G> must operate transitively on <D> in

G.operations.BlocksNoSeed( G, D ) called from

arg[1].operations.Blocks( arg[1], arg[2], [ ], OnPoints ) called from

Blocks( o, PermGroupOps.MovedPoints( o ) ) called from

Extension( bb, a ) called from

PermRefinedChain( G, Reversed( c ) ) called from

..

brk>

3. Character table of groups with strange generators:

gap> g:=Group((2,3,4,5,6),(2,6)(3,5));

Group( (2,3,4,5,6), (2,6)(3,5) )

gap> g.name:="D10";

"D10"

gap> CharTable(g);

Error, operations: product of permutation and boolean is not defined at

if x ^ (el * representatives[x]) in orbitJ ... in

FingerprintPerm( D, D.conjugacyClasses[i].representative, 1, 2, fos, fr

) called from

fun( i ) called from

List( c, function ( i ) ... end ) called from

G.operations.DxPreparation( G ) called from

DixonInit( G, opt ) called from

..

brk>

On a first glance it seems that the domain of operation is {2,3,4,5,6} instead of {1,2,3,4,5} is the reason for failing. But a similar example with the dihedral group of order 6 works: g:=Group((2,3,4),(2,3)); Group( (2,3,4), (2,3) ) gap> CharTable(g); rec( order := 6, centralizers := [ 6, 2, 3 ], orders := [ 1, 2, 3 ], classes := [ 1, 3, 2 ], irreducibles := [ [ 1, 1, 1 ], [ 1, -1, 1 ], [ 2, 0, -1 ] ], operations := CharTableOps, name := "", powermap := [ , [ 1, 1, 3 ], [ 1, 2, 1 ] ], automorphisms := Group( () ), text := "origin: Dixon's Algorithm", permuta\ tion := (2,3), group := Group( (2,3,4), (2,3) ) )

Best regards,

Olaf Neisse, Robert Boltje, Universitaet Augsburg, Germany

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