---------- Forwarded message ---------- From: Laurent Bartholdi <[EMAIL PROTECTED]> Date: Sep 18, 2007 5:08 PM Subject: Re: [GAP Forum] wreath product with a sparse permutation group To: Anvita <[EMAIL PROTECTED]>
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 <[EMAIL PROTECTED]> 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 > _______________________________________________ > Forum mailing list > [email protected] > http://mail.gap-system.org/mailman/listinfo/forum > -- 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 -- 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 _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
