Rationality problems for relation modules of dihedral groups

Abstract

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}.

arXiv commentThe title is changed slightly. The name of one of the authors, Akinari Hoshi, is corrected. Several places are improved at the suggestion of a referee. To appear in Journal of Algebra. arXiv admin note: text overlap with arXiv:1312.6738