> < ^ Date: Fri, 14 Aug 1992 02:12:55 +0200
> ^ From: Charles Wright <wright@math.uoregon.edu >
> ^ Subject: Elements of order 4 in a subgroup of order 2

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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