## Hokkaido Mathematical Journal

- Hokkaido Math. J.
- Volume 35, Number 2 (2006), 427-436.

### Mixed basic subgroups

#### 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.

#### Article information

**Source**

Hokkaido Math. J., Volume 35, Number 2 (2006), 427-436.

**Dates**

First available in Project Euclid: 29 September 2010

**Permanent link to this document**

https://projecteuclid.org/euclid.hokmj/1285766363

**Digital Object Identifier**

doi:10.14492/hokmj/1285766363

**Mathematical Reviews number (MathSciNet)**

MR2254658

**Zentralblatt MATH identifier**

1107.20048

**Subjects**

Primary: 20K21: Mixed groups

Secondary: 20K27: Subgroups

**Keywords**

mixed basic subgroup purifiable subgroup T--high subgroup splitting group

#### Citation

OKUYAMA, Takashi. Mixed basic subgroups. Hokkaido Math. J. 35 (2006), no. 2, 427--436. doi:10.14492/hokmj/1285766363. https://projecteuclid.org/euclid.hokmj/1285766363