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Greetings! I've been spending quite a bit of time working with GAP this summer, and

hope to be able to have something to show for it before long. At the moment, though,

I've run into a bug of some sort. Here's a log of what happened.

--------------

# This first chunk builds n-fold (...(C_p wr C_p) wr ... )wr C_p.

wreathPower := function (p, n)

local c, g, rc, cc, alpha;

c := CyclicGroup(AgWords, p);

g := c;

rc := RightCosets(c, TrivialSubgroup(c));

cc := Operation (c, rc, OnRight);

alpha := GroupHomomorphismByImages (c, cc, c.generators, cc.generators);

while n > 1 do g := WreathProduct (g, c, alpha); n := n-1; od;

return g;

end;;

# Now we use it to build a group whose subgroups have strange properties.

gap> A := wreathPower(2,3); # = (2wr2)wr2 Group( h, n1_1, n1_2, n1_3, n2_1, n2_2, n2_3 ) gap> B := AgSubgroup(A,[A.4*A.5*A.6],true); Subgroup( Group( h, n1_1, n1_2, n1_3, n2_1, n2_2, n2_3 ), [ n1_3*n2_1*n2_2 ] ) gap> Size(B); 2 gap> c := A.4*A.5*A.6; n1_3*n2_1*n2_2 gap> c^2; n2_2*n2_3

gap> c in B;

true

gap> Elements(B); [ IdAgWord, n1_3*n2_1*n2_2 ] gap> c^2 in B; false ----------------

Is this a known bug?

(I have applied both patches, so I know it is not fixed by either of them.)

Charley

--

wright@math.uoregon.edu

Charles R.B. Wright

Department of Mathematics

University of Oregon

Eugene, OR 97403

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