The Lind-Lehmer Constant for Some 2-Groups

摘要

The Lind-Lehmer constant of a group is the smallest positive logarithmic Lind-Mahler measure for that group. We determine this minimum for abelian groups of the form G = Z_2× H or Z_4× H when H is a 2-group whose minimal measure is known. This enables us to find the Lind-Lehmer constant of any abelian 2-group containing at least one Z_2 or Z_4 in its decomposition. This is equivalent to finding the minimal non-trivial integer group determinant for the group.