I'm gathering some information for my thesis in math (the one corresponding to the third year in European universities, I guess it's considered "Associate degree" in the American system), the central topic is the "Tarski's monster group". I agreed with my teacher that I'll mainly talk about the properties of these infinite groups, I'll quote the definition and the existence of such a group. I know the existence of a Tarski's monster group was proved by Olshanskii, but my teacher thinks it's too much to show it completely, thus I'll focus more on the properties that such groups satisfy and do not satisfy, she also said that these groups are responsible for "many counterexamples of intuitive properties that are true for finite groups but they're not true in general for infinite groups" and that I could talk about them.
My professor gave me a reference for "finiteness conditions" on infinite groups ("Finiteness Conditions and Generalized Soluble Groups" by Derek J. S. Robinson), but this book doesn't talk about Tarski's monster group, so I'm looking for some books/articles on Tarski's group construction (maybe the original Olshanskii's paper?), but mainly on their properties and those counterexamples.
Notes
I remember we also talked about solvable groups but I don't remember if they were somehow linked to the Tarski's monster group.
Update
I think I found the original Olshanskii's article: AN INFINITE GROUP WITH SUBGROUPS OF PRIME ORDERS