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41 votes
8 answers
16k views

What are some good group theory references?

I'm curious about what books people use for a group theory reference. I don't currently own a dedicated group theory book, and I think I'd find such a book very helpful in my research. What is your ...
16 votes
3 answers
2k views

Your favorite papers on geometric group theory

I would like to improve my "depth of understanding" in geometric group theory. So I am interested in short and accessible papers on subjects related to this field but which are not always ...
16 votes
3 answers
2k views

What are the main open problems in the theory of amenability of groups?

I have read the Paterson and Runde books about amenability of groups, but I do not know what are the most intriguing questions in this area today. A survey or a list of questions would be welcome.
1 vote
1 answer
312 views

Topological Invariants for Group

Let $\mathbf{Grp}$ be the category of groups and $\mathbf{Top}$ be the category of topological spaces. To each group $(G, \circ_G)$, we can associate a topological space $(G,\tau_G)$ the basis for ...
0 votes
0 answers
75 views

The set of (property) elements of a locally compact group is closed

For which properties $(P)$ is the following statement known to be true? In any locally compact group $G$, the elements of $G$ that satisfy $(P)$ form a closed subset of $G$. In other words, the ...