Special groups whose isometry relation is a finite union of cosets

Abstract

ℵ₀-stable ℵ₀-categorical linked quaternionic mappings are studied and are shown to correspond (in some sense) to special groups which are ℵ₀-stable, ℵ₀-categorical, satisfy AP(3) and have finite 2-symbol length. They are also related to special groups whose isometry relation is a finite union of cosets, which are then considered on their own, as well as their links with pseudofinite, profinite and weakly normal special groups.