Lattices of finite abelian groups
Number Theory
2023-05-04 v2 Metric Geometry
Abstract
We study certain lattices constructed from finite abelian groups. We show that such a lattice is eutactic, thereby confirming a conjecture by B\"ottcher, Eisenbarth, Fukshansky, Garcia, Maharaj. Our methods also yield simpler proofs of two known results: First, such a lattice is strongly eutactic if and only if the abelian group has odd order or is elementary abelian. Second, such a lattice has a basis of minimal vectors, except for the cyclic group of order 4.
Keywords
Cite
@article{arxiv.1810.11346,
title = {Lattices of finite abelian groups},
author = {Frieder Ladisch},
journal= {arXiv preprint arXiv:1810.11346},
year = {2023}
}
Comments
v2: Minor corrections due to referee reports, 14 pages