Abelian groups in a topos of sheaves: Torsion and essential extensions (Q1115517)

The author continues her investigation of the category of abelian groups in a localic topos, begun in Bull. Aust. Mat. Soc. 37, 43-59 (1988; Zbl 0631.18009). In the present paper she is concerned with the notions of torsion group and of essential extension. Sample positive result: torsion groups admit primary decompositions. Sample negative result: essential extensions of torsion groups need not be torsion (although conditions are given on the base locale which ensure that they are).