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;
# 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;
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.)
Charles R.B. Wright
Department of Mathematics
University of Oregon
Eugene, OR 97403