Minimal group determinants and the Lind–Lehmer problem for dihedral groups
Volume 186 / 2018
Acta Arithmetica 186 (2018), 377-395
MSC: Primary 11R06, 15B36; Secondary 11B83, 11C08, 11C20, 11G50, 11R09, 11T22, 20C05, 43A40.
DOI: 10.4064/aa180708-30-8
Published online: 5 November 2018
Abstract
We find the minimal non-trivial integer variable group determinant for any dihedral group of order less than $3.79\times 10^{47}$. We think of this as the Lind–Lehmer problem for the dihedral group. We give a complete description of the determinants for some dihedral groups including $D_{2p}$ and $D_{4p}$.
