67 citations · 358 across the 68 of their papers we have counts for
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Images of word maps in finite simple groups
Alexander Lubotzky
In response to questions by Kassabov, Nikolov and Shalev, we show that a given subset of a finite simple group is the image of some word map if and on…
Finiteness Properties and Profinite Completions
Alexander Lubotzky
In this note we show that various (geometric/homological) finiteness properties are not profinite properties. For example for every $1 \le k, \ell \le \bbn$, there exist two finite…
The Galois group of random elements of linear groups
Alexander Lubotzky, Lior Rosenzweig
Let F be a finitely generated field of characteristic zero and Γ<GL_n(F) a finitely generated subgroup. For an element g in Γ, let Gal(F(g)/ F) be the Galois group of the splitting…
Representation varieties of Fuchsian groups
Michael Larsen, Alexander Lubotzky
We estimate the dimension of varieties of the form Hom(F,G) where F is a Fuchsian group and G is a simple real algebraic group, answering along the way a question of I. Dolgachev.