16 citations · 48 across the 14 of their papers we have counts for
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Diophantine properties of nilpotent Lie groups
Menny Aka, Emmanuel Breuillard, Lior Rosenzweig +1
A finitely generated subgroup Γ of a real Lie group G is said to be Diophantine if there is β> 0 such that non-trivial elements in the word ball B_Γ(n) centered at the identity nev…
Homogeneous number of free generators
Menny Aka, Tsachik Gelander, Gregory A. Soifer
We address two questions of Simon Thomas. First, we show that for any n>2 one can find a four generated free subgroup of SLn(Z) which is profinitely dense. More generally, we show…
Arithmetic groups with isomorphic finite quotients
Menny Aka
Two finitely generated groups have the same set of finite quotients if and only if their profinite completions are isomorphic. Consider the map which sends (the isomorphism class o…
Profinite completions and Kazhdan's property (T)
Menny Aka
We show that property (T) is not profinite, that is, we construct two finitely generated residually finite groups which have isomorphic profinite completions while one admits prope…