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On approximation properties of semidirect products of groups (1312.7682v2)
Published 30 Dec 2013 in math.GR and math.DS
Abstract: Let R be a class of groups closed under taking semidirect products with finite kernel and fully residually R-groups. We prove that R contains all R-by-{finitely generated residually finite} groups. It follows that a semidirect product of a finitely generated residually finite group with a surjunctive group is surjunctive. This remained unknown even for direct products of a surjunctive group with the integers Z.
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