Conditions on Topological Gyrogroups to Embed in Topological Groups

Abstract

A topological gyrogroup is a topological space endowed with a compatible nonassociative operation, which shares several common properties with topological groups. In this thesis, we prove that every locally compact Hausdorff topological gyrogroup G can be embedded in a completely regular topological group I as a twisted subgroup. We also study properties shared by them by proving that G has property P if and only if T(G, Agyr) has property P, where P is one of the following properties: connectedness, path connectedness, and separability, and Agyr is the subgroup of the symmetric group on G generated by all the gyroautomorphisms of G.