A note on Dehn colorings and invariant factors

Abstract

If [Formula: see text] is an abelian group and [Formula: see text] is an integer, let [Formula: see text] be the subgroup of [Formula: see text] consisting of elements [Formula: see text] such that [Formula: see text]. We prove that if [Formula: see text] is a diagram of a classical link [Formula: see text] and [Formula: see text] are the invariant factors of an adjusted Goeritz matrix of [Formula: see text], then the group [Formula: see text] of Dehn colorings of [Formula: see text] with values in [Formula: see text] is isomorphic to the direct product of [Formula: see text] and [Formula: see text]. It follows that the Dehn coloring groups of [Formula: see text] are isomorphic to those of a connected sum of torus links [Formula: see text].