> < ^ Date: Mon, 04 May 1992 18:55:01 +0200
> < ^ From: Thomas Breuer <Thomas.Breuer@Math.RWTH-Aachen.DE >
> ^ Subject: [Bug in 'OperationHomomorphism']

Dear Mr. Forum,

I think I found a bug in GAP. What I tried is to work a little with
a matrix group, namely a representation of the group 'A5 x 2' as group
of symmetries of a regular icosahedron. (The session is documented
below.) The point 'p' is one of the corners of the icosahedron,
and 'orb' contains all corners. The block system 'bl' has pairs of
opposite corners as blocks, and 'op' is the permutation group
corresponding to the action on 'bl'. Up to this moment all works well,
but if I try to construct the homomorphism GAP runs into a break loop.
What is wrong here?

Thomas Breuer, Lehrstuhl D fuer Mathematik, RWTH Aachen
(sam@ernie.math.rwth-aachen.de)

```gap> b:= - E(5)^2 - E(5)^3;;
gap> mat1:= [ [ 0, 1, 0 ],
>             [ 0, 0, 1 ],
>             [ 1, 0, 0 ] ];;
gap> mat2:= 1/2 * [ [ b-1,   1,  -b ],
>                   [  -1,   b, b-1 ],
>                   [   b, b-1,   1 ] ];;
gap> g:= Group( mat1, mat2, - IdentityMat( 3 ) );;
gap> p:= [ 0, b, 1 ];
[ 0, -E(5)^2-E(5)^3, 1 ]
gap> orb:= Set( Orbit( g, p ) );
[ [ -1, 0, -E(5)^2-E(5)^3 ], [ -1, 0, E(5)^2+E(5)^3 ],
[ 0, -E(5)^2-E(5)^3, -1 ], [ 0, -E(5)^2-E(5)^3, 1 ],
[ 0, E(5)^2+E(5)^3, -1 ], [ 0, E(5)^2+E(5)^3, 1 ], [ 1, 0, -E(5)^2-E(5)^3 ],
[ 1, 0, E(5)^2+E(5)^3 ], [ -E(5)^2-E(5)^3, -1, 0 ],
[ -E(5)^2-E(5)^3, 1, 0 ], [ E(5)^2+E(5)^3, -1, 0 ], [ E(5)^2+E(5)^3, 1, 0 ]
]
gap> bl:= Blocks( g, orb );;
gap> op:= Operation( g, bl, OnSets );
Group( (1,5,3)(2,6,4), (1,2,6,3,5) )
gap> OperationHomomorphism( g, op );
Error, List assignment: <index> must be a positive int at
hom.reps[k] := i ... in
PermGroupOps.BlocksHomomorphism( G, P ) called from
P.operations.OperationHomomorphism( G, P ) called from
OperationHomomorphism( g, op1 ) called from
main loop
brk> gap>
gap>
```

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