%0 Journal Article %T Relation modules of dihedral groups %A Akinary Hoshi %A Ming-chang Kang %A Aiichi Yamasaki %J Mathematics %D 2015 %I arXiv %X Let D_n be the dihedral group of order 2n where n \ge 2, 1 \to R \to F \to D_n \to 1 be a free presentation of D_n. R^{ab}:=R/[R,R] becomes a \bm{Z}[D_n]-lattice. We will study the module structure and the rationality problem of R^{ab}. %U http://arxiv.org/abs/1503.04543v1