On Arithmetic Toroidal Groups

Abstract

Andreotti, Gherardelli, and Abe constructed toroidal groups from algebraic number fields. We call these toroidal groups arithmetic toroidal groups.  We study the algebraic structures of arithmetic toroidal groups and we show two examples of arithmetic toroidal groups where one is a quasi-Abelian variety and the other has no nonconstant meromorphic functions on it.