We prove that any countable index, universally measurable subgroup of a Polish group is open. By consequence, any universally measurable homomorphism from a Polish group into the i...
The Whitehead minimization problem consists in finding a minimum size element in the automorphic orbit of a word, a cyclic word or a finitely generated subgroup in a finite rank...
Abstract. We investigate the average-case complexity of decision problems for finitely generated groups, in particular the word and membership problems. Using our recent results on...
Ilya Kapovich, Alexei G. Myasnikov, Paul Schupp, V...
We present a new example of a partial boolean function whose one-way quantum communication complexity is exponentially lower than its one-way classical communication complexity. T...
This is an introductory survey of the emerging theory of two new classes of (discrete, countable) groups, called hyperlinear and sofic groups. They can be characterized as subgroup...