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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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