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arXiv · 1810.11346

Lattices of finite abelian groups

Frieder Ladisch
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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.

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Frieder Ladisch. 2018-10-26. Lattices of finite abelian groups. https://doi.org/10.1007/s00454-019-00163-1

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