Abstract
This chapter discusses mixed groups form the most general class of groups. At the present stage of the theory of torsion and torsion free groups, the most one might hope for is to clear up how torsion groups and torsion free groups can be put together to form a mixed group, or otherwise expressed, to describe all abelian extensions of torsion groups by torsion free groups. It is important when the mixed group splits into a direct sum of torsion free and a torsion group. The chapter presents some criteria for splitting mixed groups. Till date, no general necessary and sufficient condition is known under which every mixed group G with a given maximal torsion subgroup T and with a given torsion free factor group G/T splits. A more general problem is to determine those mixed groups in which the maximal torsion subgroup is an endomorphic image.
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