## Abstract

For an infinite Abelian group G, we give a complete description of those nonzero bounded subgroups of G which are the von Neumann radical for some Hausdorff group topology on G. If G is of infinite exponent, we prove that for every nonzero bounded subgroup H of G there exists a Hausdorff group topology τ on G such that H is the von Neumann radical of (G, τ). If G has finite exponent, we show that the following are equivalent: (i) there exists a Hausdorff group topology τ on G such that H is the von Neumann radical of (G, τ); (ii) G contains a subgroup of the form Z(exp(H))(ω). In particular, an infinite Abelian group of finite exponent admits a Hausdorff minimally almost periodic group topology if and only if all its leading Ulm-Kaplansky invariants are infinite.

Original language | English |
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Pages (from-to) | 185-199 |

Number of pages | 15 |

Journal | Topology and its Applications |

Volume | 178 |

DOIs | |

State | Published - 1 Dec 2014 |

## Keywords

- Abelian group
- Bounded Abelian group
- Dual group
- T-sequence
- Von Neumann radical

## All Science Journal Classification (ASJC) codes

- Geometry and Topology