OAI.TorsionFreeZeroDivisors.main

The theorem states that there exists a group G (in the base universe of types) satisfying four conditions at once. First, G is finitely presented. Second, G is torsion-free in the ordinary sense: whenever g^n = 1 for some positive integer n, then g = 1 (uniqueness of roots is not required). Third, G has a finite two-dimensional classifying space: there is a path-connected Hausdorff topological space X with a finite CW complex structure on all of X, having no cells of dimension above 2 and at least one 2-cell, together with a basepoint x such that G is isomorphic as a group to the fundamental group of X at x, and a contractible space E with a surjective covering map p : E → X. Fourth, the group algebra of G over the field ZMod 2 (finite formal combinations of group elements with coefficients mod 2) has zero divisors: there are nonzero elements α and β of this algebra with α·β = 0.