### Abstract

Let f : X → Y be a covering map from a connected space X onto a topological group Y and let x_{0} ∈ X be a point such that f(x_{0}) is the identity of Y: We examine if there exists a group operation on X which makes X a topological group with identity x_{0} and f a homomorphism of groups. We prove that the answer is positive in two cases: if f is an overlay map over a locally compact group Y, and if Y is locally compactly connected. In this way we generalize previous results for overlay maps over compact groups and covering maps over locally path-connected groups. Furthermore, we prove that in both cases the group structure on X is unique.

Original language | English |
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Pages (from-to) | 241-267 |

Number of pages | 27 |

Journal | Fundamenta Mathematicae |

Volume | 238 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2017 |

### Keywords

- Abelian group
- Compact group
- Compactly connected space
- Covering homomorphism
- Covering map
- Locally compact group
- Locally compactly connected space
- Overlay map
- Topological group

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Eda, K., & Matijević, V. (2017). Existence and uniqueness of group structures on covering spaces over groups.

*Fundamenta Mathematicae*,*238*(3), 241-267. https://doi.org/10.4064/fm990-10-2016