67 citations · 528 across the 47 of their papers we have counts for
5 papers · 2 filters
Words with few values in finite simple groups
Martin Kassabov, Nikolay Nikolov
We construct words with small image in a given finite alternating or unimodular group. This shows that word width in these groups is unbounded in general.
Algebraic properties of profinite groups
Nikolay Nikolov
Recently there has been a lot of research and progress in profinite groups. We survey some of the new results and discuss open problems. A central theme is decompositions of finite…
Product decompositions in finite simple groups
Martin Liebeck, Nikolay Nikolov, Aner Shalev
We propose a general conjecture on decompositions of finite simple groups as products of conjugates of an arbitrary subset. We prove this conjecture for bounded subsets of arbitrar…
On the growth of Betti numbers of locally symmetric spaces
Miklos Abert, Nicolas Bergeron, Ian Biringer +4
We announce new results concerning the asymptotic behavior of the Betti numbers of higher rank locally symmetric spaces as their volumes tend to infinity. Our main theorem is a uni…
Generators and commutators in finite groups; abstract quotients of compact groups
Nikolay Nikolov, Dan Segal
Let N be a normal subgroup of a finite group G. We prove that under certain (unavoidable) conditions the subgroup [N,G] is a product of commutators [N,y] (with prescribed values of…