Albrecht Boettcher, Lenny Fukshansky, Stephan Ramon Garcia, Hiren Maharaj
Published 2014-06-30, updated 2014-07-21Version 2
This paper is devoted to the study of lattices generated by finite Abelian groups. Special species of such lattices arise in the exploration of elliptic curves over finite fields. In case the generating group is cyclic, they are also known as the Barnes lattices. It is shown that for every finite Abelian group with the exception of the cyclic group of order four these lattices have a basis of minimal vectors. Another result provides an improvement of a recent upper bound by Min Sha for the covering radius in the case of the Barnes lattices. Also discussed are properties of the automorphism groups of these lattices.
The $h$-critical number of finite abelian groups
Cross Number Invariants of Finite Abelian Groups
Lattices of finite abelian groups
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