Hi, my name is Valeriia, I'm a second year mathematics undergrad at the 
University of Oxford, UK and I'd be really interested to work on a group 
theory project. I am trying to work out what features still need to be 
implemented and which would be the most useful at this stage.

>From what reading I've done in the past several days, it looks like not 
much is implemented for subgroups and quotient groups. There is a #TODO 
note in fp_groups (line 162) that suggests that at present a subgroup can 
only be specified as a set of generators but can't be made into a group in 
its own right. This obviously needs fixing. Also, Gaurav Dhingra's proposal 
from last year 
(https://github.com/sympy/sympy/wiki/GSoC-2016-Application-Gaurav-Dhingra:-Group-Theory)
 
included plans to implement a `factor_group()` function to compute quotient 
groups but that was never realised, if I'm not mistaken (at least I didn't 
find anything in the files related to groups in the combinatorics module) 
so that's another thing that needs work, as well as computing normal 
closures, centres, centralizers and normalizers. I'm also vaguely thinking 
of implementing something to do with group homomorphisms and things though 
I don't have a clear plan for that yet (I'm working on it).
Apparently, there's also been some talk of moving group things from 
combinatorics to a separate module which also hasn't happened.

What do you think? And what other things would be good to 
implement/fix/improve?

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