Hi, I'm Gaurav Dhingra, i will hopefully be a GSoC applicant this year. I 
want to discuss the possibilities for what "should"
i do in regards to extend the Group Theory in SymPy. I saw there is some 
questions on ideas page I want to discuss the
Group Theory idea given on the Idea's page.
https://github.com/sympy/sympy/wiki/GSoC-2015-Ideas#group-theory

I also made a wiki: 
https://github.com/sympy/sympy/wiki/GSoC-2016-Application-Gaurav-Dhingra:-Group-Theory
 
.
I think it will be really good if we could first discuss the things that 
can be done in order. Since implementation of certain
groups may require the implementation of others or certain `class`. Example 
we don't yet have a `Group` class from which
all the `groups` could be derived, though this class in itself will be of 
very little use, 

since Prof. Kalevi said:

> I think that may be too general for practical purposes. Besides, many 
groups are infinite and the corresponding sets are not easily described.

In particular i am sure that i will start working with the implementation 
of `FreeGroup` and `Finitely Presented Groups` (only sure that this can be 
done, 
but how to do this is still to be worked upon in detail), this itself will 
take quite sometime, but can something more be done?

I feel quite positive that we should be following the `GAP` (gap-system.org) 
for what algorithms be used. 

--
Gaurav

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