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.)

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.
> >
> > --
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>

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