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...
We consider matrix groups, specified by a list of generators, over finite fields. The two most basic questions about such groups are membership in and the order of the group. Even...
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 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...
We give necessary and sufficient conditions for the first-order theory of a finitely presented abelian lattice-ordered group to be decidable. We also show that if the number of gen...