A. Lubotzky

activity

20002025

most citedFinite Simple Groups as Expanders

67 citations · 358 across the 68 of their papers we have counts for

collaborators

Showing 2004 · math.GRShow all

4 papers · 2 filters

math.GR2004

Counting congruence subroups

D. Goldfeld, A. Lubotzky, L. Pyber

Let $Γ$ denote the modular group $S L (2, Z)$ and $C_{n} (Γ)$ the number of congruence subgroups of $Γ$ of index at most $n$ . We prove that $\lim\limits_{n\to \infty} \frac{\log C_n…

math.GR2004

Subgroup growth of lattices in semisimple Lie groups

A. Lubotzky, N. Nikolov

We give very precise bounds for the congruence subgroup growth of arithmetic groups. This allows us to determine the subgroup growth of irreducible lattices of semisimple Lie group…

math.GR2004★ 13 cited

Counting primes, groups and manifolds

D. Goldfeld, A. Lubotzky, N. Nikolov +1

Let $Λ = SL_{2} (Z)$ be the modular group and let $c_{n} (Λ)$ be the number of congruence subgroups of $Λ$ of index at most $n$ . We prove that $\lim\limits_{n\to \infty} \fr…

math.GR2004★ 30 cited

Finite Groups and Hyperbolic Manifolds

M. Belolipetsky, A. Lubotzky

The isometry group of a compact n-dimensional hyperbolic manifold is known to be finite. We show that for every n > 2, every finite group is realized as the full isometry group of…