You can lift elements via the quotient map to get representatives of each coset. I'm not sure that this is wrapped in Sage, but using gap directly you have:
sage: Pgap = p._libgap_() sage: Ngap = N._libgap_() sage: phi = Pgap.NaturalHomomorphismByNormalSubgroup(Ngap); phi [ (2,3,4,5,6,7) ] -> [ f1^2 ] sage: PN = phi.ImagesSource() # the quotient as an isomorphic group sage: preimages_gens = [phi.PreImagesRepresentative(g) for g in PN.GeneratorsOfGroup()] sage: preimages_gens [(2,4,6)(3,5,7)] sage: all_preimages = [phi.PreImagesRepresentative(g) for g in PN.List()] sage: all_preimages [(), (2,4,6)(3,5,7), (2,6,4)(3,7,5)] David On Sat, Feb 3, 2024 at 10:58 AM 'Ruchit Jagodara' via sage-devel < sage-devel@googlegroups.com> wrote: > I think this is giving a group isomorphic to the actual quotient group but > I need the actual quotient group. Therefor, I don't know how to find that > exact group. Below is one example, > > sage: p = PermutationGroup([(2,3,4,5,6,7)]) > sage: N = p.minimal_normal_subgroups()[0] > sage: N > Subgroup generated by [(2,5)(3,6)(4,7)] of (Permutation Group with > generators [(2,3,4,5,6,7)]) > sage: N.list() > [(), (2,5)(3,6)(4,7)] > sage: p.quotient(N) > Permutation Group with generators [(1,2,3)] > sage: _.list() > [(), (1,2,3), (1,3,2)] > > If this is the collection of representative elements(for cosets) then > ``1`` should not be in any of the permutations. > > I need a quotient group structure whose elements(the cosets) have the > representative element (from the original group) and the normal subgroup > (which was used to create the quotient group) as their properties or > available in some other form. > On Friday, January 19, 2024 at 10:33:21 PM UTC+5:30 Dima Pasechnik wrote: > >> >> >> On 19 January 2024 15:18:45 GMT, 'Ruchit Jagodara' via sage-devel < >> sage-...@googlegroups.com> wrote: >> >In case my questions have caused any confusion, I am rephrasing them as >> >below. >> > >> >I have a group G and its minimal normal subgroup N. >> > >> >I want to find G/N. Do you know how I can do that? (I also want G/N to >> be >> >an object of the same class as G.) >> >> It's G.quotient(N), no? >> >> > >> >My another question is: How can I find the group operation of a group G? >> >On Thursday, January 18, 2024 at 7:13:50 PM UTC+5:30 Dima Pasechnik >> wrote: >> > >> >> On Thu, Jan 18, 2024 at 11:39 AM 'Ruchit Jagodara' via sage-devel >> >> <sage-...@googlegroups.com> wrote: >> >> > >> >> > Actually, that won't work according to the implementation. >> >> >> >> sorry, I don't understand what won't work. >> >> Did you mean to ask a different question? >> >> >> >> > Can you please take a look at the code I wrote (although I have not >> >> written it according to codestyle of sage, yet. But I will do that >> when the >> >> code starts working.), where minimum_generating_set is the main >> function? >> >> > >> >> > Link- >> >> >> https://github.com/RuchitJagodara/sage/blob/8b642329b6d579c536511d5f1d1511fb842c9c54/src/sage/groups/libgap_wrapper.pyx#L405C1-L513C1 >> >> > >> >> > I have implemented this code according to the research paper. >> >> >> >> Sorry, what paper are you talking about? >> >> >> >> >> >> > The algorithm can find the minimum generating set in polynomial >> time, >> >> which is very cool! So, I thought it would be good to implement this >> in >> >> Sage, especially since the paper has been recently published. >> >> > >> >> > I've almost completed the code, but I'm unsure about how to find the >> >> Quotient group and its representative elements. I need help with this. >> >> > >> >> > I've outlined my doubts in the code, which you can see in the >> following >> >> link:- >> >> > >> >> > >> >> >> https://github.com/RuchitJagodara/sage/blob/8b642329b6d579c536511d5f1d1511fb842c9c54/src/sage/groups/libgap_wrapper.pyx#L478-L486 >> >> > >> >> > GAP has a function named RightCosets that can be used to form a >> quotient >> >> group, but there is a problem: how can I find representative elements >> of >> >> that group? Additionally, how can I create a Quotient group using >> >> RightCosets in Sage, given that the algorithm uses a recursive call, >> and >> >> the quotient group must have the ParentLibGAP.minimum_generating_set >> >> function? >> >> > On Wednesday, January 17, 2024 at 2:35:55 PM UTC+5:30 Dima Pasechnik >> >> wrote: >> >> >> >> >> >> Functions such as Group(), PermutationGroup() take such lists as >> inputs. >> >> >> >> >> >> >> >> >> On 17 January 2024 06:35:07 GMT, 'Ruchit Jagodara' via sage-devel < >> >> sage-...@googlegroups.com> wrote: >> >> >>> >> >> >>> And to implement the function, I want a function that takes a list >> of >> >> generators and returns a group. Does anyone know of any function that >> can >> >> do this? >> >> >>> On Friday, January 12, 2024 at 8:38:18 PM UTC+5:30 Ruchit Jagodara >> >> wrote: >> >> >>>> >> >> >>>> I am implementing the minimum_generating_set function in Sage, >> but I >> >> am facing some issues, such as where I should implement that function >> as my >> >> implementation uses some gap methods. And I found one class >> ParentLibGAP >> >> which can be used for this but I am not sure because I found that >> >> PermutationGroup class is not derived from this class so if I >> implement >> >> this function here then function will not be available for this group >> (And >> >> I don't know if there are many more), plus I have to use some >> functions of >> >> GroupMixinLibGAP class, so can you please suggest me a location or any >> fix >> >> for this. >> >> > >> >> > -- >> >> > You received this message because you are subscribed to the Google >> >> Groups "sage-devel" group. >> >> > To unsubscribe from this group and stop receiving emails from it, >> send >> >> an email to sage-devel+...@googlegroups.com. >> >> > To view this discussion on the web visit >> >> >> https://groups.google.com/d/msgid/sage-devel/db166267-6491-42e3-bc58-01ea447a5c9bn%40googlegroups.com >> >> . >> >> >> > >> > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-devel/2119b5d7-b98d-4edb-acb7-3e7704cbaffen%40googlegroups.com > <https://groups.google.com/d/msgid/sage-devel/2119b5d7-b98d-4edb-acb7-3e7704cbaffen%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. 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