Profinite genus of fundamental groups of compact flat manifolds with the cyclic holonomy group of square-free order

Abstract In this article, we study the extent to which an n -dimensional compact flat manifold with the cyclic holonomy group of square-free order may be distinguished by the finite quotients of its fundamental group. In particular, we display a formula for the cardinality of profinite genus of the fundamental group of an n -dimensional compact flat manifold with the cyclic holonomy group of square-free order.