One of the main reasons I only supervised one PhD student is that I find it hard to find an appropriate topic for a PhD project. A good approach, in my view, is to have on the one hand a list of interesting questions and on the other hand rich enough family of examples so that the student would be able to find answers to some of these questions for some of the examples. I have many questions that I would like to know the answer for interesting examples of residually-finite groups, in particular, for finitely presented ones. Unfortunately, I am very far from being an expert on this topic.
Is there anywhere I can find a list of examples of families of residually-finite groups, preferably, including some of their interesting properties?
Best Answer
Here are some examples of finitely presented residually finite groups. All these can be easily found in arXiv.
Small cancellation groups (Agol and Wise) although these turned out to be linear.
Ascending HNN extensions of free groups (Borisov - Sapir). Some of them are not linear.
Some complicated solvable residually finite groups (Kharlampovich-Myasnikov-Sapir). These are not linear. At the beginning of that paper, there is a survey of various constructions of finitely presented residually finite (and non-residually finite) groups.