Embedding of locally compact Hausdoff topological gyrogroups in topological groups

A topological gyrogroup is a topological space endowed with a compatible nonassociative operation, which shares several common properties with topological groups. In this article, we prove that every locally compact Hausdorff topological gyrogroup G can be embedded in a completely regular topological group Gamma as a twisted subset. We also study properties shared by them by proving that G has property P if and only if Gamma has property P, where P is one of the following properties: connectedness, path connectedness, and separability. (C) 2020 Elsevier B.V. All rights reserved.