On subgroups of semi-abelian varieties defined by difference equations

© 2017 American Mathematical Society.We study the induced structure on definable groups in existentially closed difference fields. If G is a definable subgroup of a semi-abelian variety, orthogonal to every definable field, we show that G is stable and stably embedded; every definable subset of Gn is a Boolean combination of cosets of definable subgroups of Gn, and Gn has at most countably many definable subgroups. This generalises to positive characteristic earlier results of the authors.