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8h
revised What finitely generated amenable groups are known to be LERF?
Improved formatting and organization so that it is easier to understand
1d
comment Can two non-abelian groups have an abelian product or coproduct?
You could have instead $1_G: G \to G$, and $H \to G$ the trivial morphism.
1d
answered Can two non-abelian groups have an abelian product or coproduct?
1d
revised What finitely generated amenable groups are known to be LERF?
Changed to actually answer the question! (Was doing a bit too much research and forgot the question...)
1d
answered What finitely generated amenable groups are known to be LERF?
1d
comment What finitely generated amenable groups are known to be LERF?
Just to be clear, these groups won't be LERF in general, but I would be a tad surprised if there was not a decent amount of examples, or a nice construction out there to make such examples.
1d
comment What finitely generated amenable groups are known to be LERF?
I am not sure, but would check around for solvable groups of exponential growth, since they are amenable, infinite, and not nilpotent, so LERF is the only thing to look for.
Jul
23
comment Presentations of the unity group
Do you know where this class of examples came from? I have seen it attributed to Neumann a couple of places, but I am not sure where he initially showed this class of examples.
Jul
23
comment Presentations of the unity group
I suspect you might be looking for this construction but I have not been able to find where Neumann initially used it.
Jul
23
revised Do uncountable groups have generating sets where you can find elements of arbitrarily long length, and what are conditions to guarantee that?
Added more information, improved formatting, added some conditions for a group to have the property the OP is looking for.
Jul
22
comment Do uncountable groups have generating sets where you can find elements of arbitrarily long length, and what are conditions to guarantee that?
I will continue to look around for general conditions, I would be surprised if there were "really general" conditions, so you (@Sam) might benefit from being more specific about the sort of groups you are looking at, maybe ask a different question about that group. I suspect something like "being close to free" would be an area to look into (maybe freely acting on some spaces). Prop 2.4 in Yves's paper above could be useful to you, it gives some equivalences between some properties involving Cayley bounded, so maybe the negation of those statements could be useful to you.
Jul
22
revised Do uncountable groups have generating sets where you can find elements of arbitrarily long length, and what are conditions to guarantee that?
I accidentially put an outdated version of Cornulier's paper in the link
Jul
22
revised Do uncountable groups have generating sets where you can find elements of arbitrarily long length, and what are conditions to guarantee that?
edited title
Jul
22
revised Do uncountable groups have generating sets where you can find elements of arbitrarily long length, and what are conditions to guarantee that?
added 6 characters in body; edited title
Jul
22
answered Do uncountable groups have generating sets where you can find elements of arbitrarily long length, and what are conditions to guarantee that?
Jul
21
reviewed Approve Given that $p$ is an odd prime, is the GCD of any two numbers of the form $2^p + 1$ always equal to $3$?
Jul
21
comment Do uncountable groups have generating sets where you can find elements of arbitrarily long length, and what are conditions to guarantee that?
Do you know if it is true for countable groups, or are you just interested in the uncountable case? If you do know for countable groups, do you have a short proof or reference?
Jul
21
comment Do uncountable groups have generating sets where you can find elements of arbitrarily long length, and what are conditions to guarantee that?
Are you talking about finitely generated groups? If so, and your group is infinite, then yes you can, since there are only finitely many elements less than or equal to some length, when you consider a finite generating set.
Jul
1
reviewed Approve Unusual result to the addition
Jun
25
reviewed Reject Question on Math.floor on negative number