Dear GAP community,Kindly appealing for your help,I have a permutation
representation of a group G, and my intention is to get the generators of the
group in Matrix form over GF(3),I am trying, gap> G := Group
(GeneratorsOfGroup);;
gap> M := PermGModule (G, GF(3));The system returns an error Variable
'PermGModule' must have a value not in any function at ...How do i go about it
Best Regards
David.
Sent from Yahoo Mail on Android
On Mon, 29 Jun 2020 at 13:06, Dima Pasechnik<[email protected]>
wrote: Dear all,
> How can i generate a group e.g "Sp6(2)" as a matrix group by 7 * 7 matrices,
> then generate "S8" as a matrix group inside Sp6(2) by 7 * 7 matrices using
> GAP prog.
gap> G:=GeneralOrthogonalGroup(7,2); # use the fact that Sp(6,2)=O(7,2)
GO(0,7,2)
gap> o:=Orbits(G, GF(2)^7,OnLines);;
gap> List(o,Size); # in this representation S8 fixes a hyperplane, not a vector
[ 1, 63, 63, 1 ]
gap> Gt:=Group(List(GeneratorsOfGroup(G),TransposedMat));
<matrix group with 2 generators>
gap> ot:=Orbits(Gt, GF(2)^7,OnLines);;
gap> List(ot,Length); # the stabiliser of a vector in 3rd orbit is S8
[ 1, 63, 36, 28 ]
gap> s8:=Stabilizer(Gt,ot[3][1],OnLines); # here it is.
<matrix group of size 40320 with 3 generators>
Hope this helps
Dima
On Mon, Jun 29, 2020 at 07:32:51AM +0000, David Musyoka wrote:
> Dear Forum, Dear Alexander Hulpke,
> Given a group G, and and a vector space V of dimension n over GF(q), i am abe
> to compute the orbit Lengths of V under action of G using the following GAP
> commands:
> V:=FullRowSpace(GF(q),n);Orb:=OrbitLengths(G,V)
> My question is, how then do i compute the corresponding point stabilizers
> (which are subgroups of G) for the orbits using GAP.
> Thank you team in advance.
> David.
> Sent from Yahoo Mail on Android
>
> On Sun, 21 Jun 2020 at 22:47, David Musyoka<[email protected]> wrote:
> Dear Alexander Hulpke,Dear Forum.
> Thank You very much.
>
> Sent from Yahoo Mail on Android
>
> On Sun, 21 Jun 2020 at 19:48,
>Hulpke,Alexander<[email protected]> wrote: Dear Forum, Dear Marc
>David Musyoka,
>
> On Jun 20, 2020, at 00:22, David Musyoka <[email protected]> wrote:
> Deat all,
> Kind request to this team, i am new to GAP and i wish to be assisted in the
> following,
> How can i generate a group e.g "Sp6(2)" as a matrix group by 7 * 7 matrices,
> then generate "S8" as a matrix group inside Sp6(2) by 7 * 7 matrices using
> GAP prog.
>
> I wish that am assisted on how to execute the same step by step and the
> matrix generators for the two groups be listed.
>
>
> Yes, I also often wish that someone would assist me in every step and provide
> me with the full result.
> Anyhow, in this case (the algorithm is exponential time and attempts will
> fail if groups are too large, or if the subgroup to be embedded needs many
> generators) `IsomorphicSubgroups` seems to do the trick in a few minutes.
> gap> G:=SP(6,2);Sp(6,2)gap> emb:=IsomorphicSubgroups(G,SymmetricGroup(8)); #
> finds embeddings from S8 into G[ [ (1,8)(2,7)(3,5)(4,6), (1,8,4,7,3)(5,6) ]
> -> [ <an immutable 6x6 matrix over GF2>, <an immutable 6x6 matrix over
> GF2> ] ]gap> sub:=Image(emb[1]);<matrix group with 2 generators>
> So there is one class of subgroups and `sub` is one (not necessarily the
> nicest one) representative.
> Of course this is computational overkill. The more sensible way would be to
> produce the matrix representation (as reduced permutation representation),
> find the form that it stabilizes, and then conjugate that form to the one
> used for Sp.
> Oh, here are the explicit matrix generators :-)
> gap> GeneratorsOfGroup(sub);[ <an immutable 6x6 matrix over GF2>, <an
> immutable 6x6 matrix over GF2> ]
> (You can use `Print` or `Display` on each of them to see them with numbers.)
> All the best,
> Alexander Hulpke
> -- Colorado State University, Department of Mathematics,
> Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
> email: [email protected],
> http://www.math.colostate.edu/~hulpke
>
>
>
> _______________________________________________
> Forum mailing list
> [email protected]
> https://mail.gap-system.org/mailman/listinfo/forum
Dear all,
> How can i generate a group e.g "Sp6(2)" as a matrix group by 7 * 7 matrices,
> then generate "S8" as a matrix group inside Sp6(2) by 7 * 7 matrices using
> GAP prog.
gap> G:=GeneralOrthogonalGroup(7,2); # use the fact that Sp(6,2)=O(7,2)
GO(0,7,2)
gap> o:=Orbits(G, GF(2)^7,OnLines);;
gap> List(o,Size); # in this representation S8 fixes a hyperplane, not a vector
[ 1, 63, 63, 1 ]
gap> Gt:=Group(List(GeneratorsOfGroup(G),TransposedMat));
<matrix group with 2 generators>
gap> ot:=Orbits(Gt, GF(2)^7,OnLines);;
gap> List(ot,Length); # the stabiliser of a vector in 3rd orbit is S8
[ 1, 63, 36, 28 ]
gap> s8:=Stabilizer(Gt,ot[3][1],OnLines); # here it is.
<matrix group of size 40320 with 3 generators>
Hope this helps
Dima
On Mon, Jun 29, 2020 at 07:32:51AM +0000, David Musyoka wrote:
> Dear Forum, Dear Alexander Hulpke,
> Given a group G, and and a vector space V of dimension n over GF(q), i am abe
> to compute the orbit Lengths of V under action of G using the following GAP
> commands:
> V:=FullRowSpace(GF(q),n);Orb:=OrbitLengths(G,V)
> My question is, how then do i compute the corresponding point stabilizers
> (which are subgroups of G) for the orbits using GAP.
> Thank you team in advance.
> David.
> Sent from Yahoo Mail on Android
>
> On Sun, 21 Jun 2020 at 22:47, David Musyoka<[email protected]>
> wrote: Dear Alexander Hulpke,Dear Forum.
> Thank You very much.
>
> Sent from Yahoo Mail on Android
>
> On Sun, 21 Jun 2020 at 19:48,
> Hulpke,Alexander<[email protected]> wrote: Dear Forum, Dear
> Marc David Musyoka,
>
> On Jun 20, 2020, at 00:22, David Musyoka <[email protected]> wrote:
> Deat all,
> Kind request to this team, i am new to GAP and i wish to be assisted in the
> following,
> How can i generate a group e.g "Sp6(2)" as a matrix group by 7 * 7 matrices,
> then generate "S8" as a matrix group inside Sp6(2) by 7 * 7 matrices using
> GAP prog.
>
> I wish that am assisted on how to execute the same step by step and the
> matrix generators for the two groups be listed.
>
>
> Yes, I also often wish that someone would assist me in every step and provide
> me with the full result.
> Anyhow, in this case (the algorithm is exponential time and attempts will
> fail if groups are too large, or if the subgroup to be embedded needs many
> generators) `IsomorphicSubgroups` seems to do the trick in a few minutes.
> gap> G:=SP(6,2);Sp(6,2)gap> emb:=IsomorphicSubgroups(G,SymmetricGroup(8)); #
> finds embeddings from S8 into G[ [ (1,8)(2,7)(3,5)(4,6), (1,8,4,7,3)(5,6) ]
> -> [ <an immutable 6x6 matrix over GF2>, <an immutable 6x6 matrix over
> GF2> ] ]gap> sub:=Image(emb[1]);<matrix group with 2 generators>
> So there is one class of subgroups and `sub` is one (not necessarily the
> nicest one) representative.
> Of course this is computational overkill. The more sensible way would be to
> produce the matrix representation (as reduced permutation representation),
> find the form that it stabilizes, and then conjugate that form to the one
> used for Sp.
> Oh, here are the explicit matrix generators :-)
> gap> GeneratorsOfGroup(sub);[ <an immutable 6x6 matrix over GF2>, <an
> immutable 6x6 matrix over GF2> ]
> (You can use `Print` or `Display` on each of them to see them with numbers.)
> All the best,
> Alexander Hulpke
> -- Colorado State University, Department of Mathematics,
> Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
> email: [email protected],
> http://www.math.colostate.edu/~hulpke
>
>
>
> _______________________________________________
> Forum mailing list
> [email protected]
> https://mail.gap-system.org/mailman/listinfo/forum
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