67 citations · 358 across the 68 of their papers we have counts for
58 papers · 1 filter
Characteristic Subgroup Growth
Liam Hanany, Alexander Lubotzky
Let denote the number of characteristic subgroups of index at most in a finitely generated group . In response to a question of I. Rivin we show that if…
Non-congruence presentations of finite simple groups
William Y. Chen, Alexander Lubotzky, Pham Huu Tiep
We prove two results on some special generators of finite simple groups and use them to prove that every non-abelian finite simple group admits a non-congruence presentation (a…
Some remarks on Grothendieck pairs
Andrei Jaikin-Zapirain, Alexander Lubotzky
We revisit the paper of Alexander Grothendiek where he introduced Grothendieck pairs and discuss the relation between profinite rigidity and left/right Grothendieck rigidity. We al…
Finite simple characteristic quotients of the free group of rank 2
William Y. Chen, Alex Lubotzky, Pham Huu Tiep
In this paper we describe how to explicitly construct infinitely many finite simple groups as characteristic quotients of the rank 2 free group . This shows that a "baby" vers…
Stability and instability of lattices in semisimple groups
Uri Bader, Alexander Lubotzky, Roman Sauer +1
Using cohomological methods, we show that lattices in semisimple groups are typically stable with respect to the Frobenius norm but not with respect to the operator norm.
Asymptotic Cohomology and Uniform Stability for Lattices in Semisimple Groups
Lev Glebsky, Alexander Lubotzky, Nicolas Monod +1
It is, by now, classical that lattices in higher rank semisimple groups have various rigidity properties. In this work, we add another such rigidity property to the list: uniform s…