# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 35 (2006) pp.427-436

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### Abstract

Every torsion abelian group has basic subgroups and all its basic subgroups are isomorphic. We extend the concept of basic subgroups from torsion abelian groups to arbitrary abelian groups. The generalized basic subgroups are called mixed basic subgroups. An example of a mixed group is given in which not all mixed basic subgroups are isomorphic. This example also shows that a mixed basic subgroup of a splitting group need not be splitting.

MSC(Primary) 20K21 20K27 mixed basic subgroup, purifiable subgroup, T--high subgroup, splitting group