DOI: 10.1515/advgeom-2026-0020. ISSN: 1615-7168
Non-cofinite two-dimensional integral braces
Wolfgang RumpAbstract
Non-cofinite integral braces of dimension two are classified, completing the classification of two-dimensional affine crystallographic groups which arise as adjoint group of a brace. It is shown that there are six infinite sequences of such braces and five sequences of associated flat affine manifolds. Rédei and Cohn obtained four isomorphism types of groups which allow a factorization into a pair of infinite cyclic groups. Only three of them arise as adjoint groups of non-cofinite integral braces. One of the six sequences of non-cofinite integral braces is exceptional in the sense that it consists of braces whose adjoint group is not factorizable into a pair of infinite cyclic groups.