Fwd: [GAP Forum] wreath product with a sparse permutation group

[Laurent Bartholdi]

---------- Forwarded message ----------
From: Laurent Bartholdi <laurent.bartholdi at gmail.com>
Date: Sep 18, 2007 5:08 PM
Subject: Re: [GAP Forum] wreath product with a sparse permutation group
To: Anvita <anvita21 at gmail.com>


Dear Anvita,
This is definitely a bug in the documentation. WreathProduct() of
permutation groups constructs the wreath product with the permutation
group G, acting on [1..LargestMovedPoint(G)].

There has been some talk on extending / generalizing the construction
of WreathProduct; however, I'm sure that in this precise case the
documentation, and not the code, will be changed.

Best wishes, Laurent

On 9/18/07, Anvita <anvita21 at gmail.com> wrote:
> Dear Forum,
>
> The manual says that the function
>
> WreathProduct( G, P )
>
> constructs the wreath product of the group G with
> the permutation group P (acting on its MovedPoints).
> Presumably, this means that the resulting group
> should have size
>
> |G|^n * |P|,
>
> where n = Size(MovedPoints(P)).
> However, this is not so in the case where P is a
> "sparse" permutation group. For example:
>
> --------------------------------------
> gap> R:=Group((1,3,5));
> Group([ (1,3,5) ])
> gap> MovedPoints(R);
> [ 1, 3, 5 ]
> gap> Size(last);
> 3
> gap> WreathProduct(CyclicGroup(5),R);
> <group of size 9375 with 4 generators>
> gap> 5^3*3;
> 375
> gap> 5^5*3;
> 9375
> --------------------------------------
>
> Is this the expected behavior?
>
> Thank you,
> Anvita
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>


--
Laurent Bartholdi          \  laurent.bartholdi<at>gmail<dot>com
EPFL SB SMA IMB MAD         \    Téléphone: +41 21-6935458
Station 8                    \ Secrétaire: +41 21-6935471
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-- 
Laurent Bartholdi          \  laurent.bartholdi<at>gmail<dot>com
EPFL SB SMA IMB MAD         \    Téléphone: +41 21-6935458
Station 8                    \ Secrétaire: +41 21-6935471
CH-1015 Lausanne, Switzerland \      Fax: +41 21-6930339