The solubility of certain decision problems in arithmetic and algebra
Fritz J. Grunewald, Dan Segal · Bulletin of the American Mathematical Society · 1979
Introduction.In contrast to the negative solution of Hubert's 10th problem, we show that a certain type of Diophantine question connected with algebraic groups is effectively decidable.Applications include the solution of the conjugacy problem in all arithmetic groups and the solution of the isomorphism problem for finitely generated nilpotent groups.Results.We have constructed some rather general algorithms, which can (in theory) be applied in diverse situations.Let us describe them.A. ARITHMETIC GROUPS.Let G be an algebraic subgroup of GL n , defined