The existence of suitable sets in locally compact strongly topological gyrogroups

Abstract: A subset $S$ of a topological gyrogroup $G$ is said to be a {\it suitable set} for $G$ if the identity element $0$ is the unique accumulation point of $S$ and $\langle S\rangle$ is dense in $G$. In this paper, it is proved that every locally compact strongly topological gyrogroup has a suitable set, which gives an affirmative answer to a question posed by F. Lin, et al. in \cite{key14}.