You will need to talk with the former students and mentors of the past
GSoC group theory projects about the proposal specifics. I don't
personally have much knowledge of the state of the group theory
module, so I can't help you much there.

My generic advice (also applies to any other potential GSoC student
reading) would be

- Take a look at previous successful proposals on the wiki to see what
a good proposal looks like.
- Focus on your pull request(s) for the patch requirement. We take the
patch requirement into high consideration as it shows us how capable
you are of actually completing your project.
- Try to familiarize yourself with the codebase so that you have a
good understanding of what is already implemented, and what will need
to be done for your project.
- Make sure you've read through and understand our student
instructions 
(https://github.com/sympy/sympy/wiki/GSoC-2019-Student-Instructions)
and application template
(https://github.com/sympy/sympy/wiki/GSoC-2019-Application-Template).
- Interact with the community here, on the issue tracker, and on gitter.

Aaron Meurer

On Fri, Mar 8, 2019 at 2:15 PM Vinayak Shukla <[email protected]> wrote:
>
> Hey there, Aaron.
> I have gone through the documentation as well as the previous work done in 
> the field by earlier GSoCers. It has provided me a lot of insight as to how 
> to go about my project proposal. I think I would like to work mainly on 
> figuring out the kernels of homomorphisms with infinite domains; checking if 
> two groups are isomorphic; automorphisms as these topics seem to mesh 
> together really well if someone starts implementing one of these.
> Apart from these, I would like to take up probability integration solving if 
> possible as well. Any suggestions from your side as to how should I start 
> building a good proposal?
> Thank you.
> Vinayak.
>
> On Friday, March 8, 2019 at 12:17:31 AM UTC+5:30, Aaron Meurer wrote:
>>
>> I would start with the reports from previous year's projects (on the
>> wiki), as well as the codebase, to see what is already implemented.
>>
>> Aaron Meurer
>>
>> On Thu, Mar 7, 2019 at 11:13 AM Vinayak Shukla <[email protected]> wrote:
>> >
>> > Although I have started reading about the previous work done on 
>> > Computational Group theory as part of GSoC in the previous years, can 
>> > someone guide me as to how should I progress with this? I am mainly 
>> > interested in implementing the kernel of homomorphisms in the infinite 
>> > domain and group isomorphism algorithms.
>> > Thanks.
>> > Vinayak Shukla
>> >
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