Some results between the properties of strongly topological gyrogroups and the properties of their remainders are established. In particular, if a strongly topological gyrogroup G is non-locally compact and G has a first-countable remainder, then \(\chi (G)\le \omega _{1}\), \(\omega (G)\le 2^{\omega }\) and \(|bG|\le 2^{\omega _{1}}\). Moreover, it is proved that the property of paracompact p-space of a strongly topological gyrogroup G is equivalent with G having a Lindelöf remainder in a compactification. By this result, we prove that if H is a dense subspace of a strongly topological gyrogroup G which is locally pseudocompact and not locally compact, then every remainder of H is pseudocompact. Furthermore, if a strongly topological gyrogroup G has countable pseudocharacter and G is non-metrizable, then all remainders of G are pseudocompact. These two results give partial answers to a question posed by Arhangel’ skiǐ and Choban, see (Topol Appl 157:789–799, 2010, Problem 5.1). Finally, it is shown that the Lindelöf property of a non-locally compact strongly topological gyrogroup G is equivalent with having a remainder with subcountable type for some compactifications of G.

建立了强拓扑陀螺群性质与其余数性质之间的一些结果。特别地，如果一个强拓扑陀螺群 G是非局部紧的并且G有一个第一可数余数，那么\(\chi (G)\le \omega _{1}\) , \(\omega (G)\ le 2^{\omega }\)和\(|bG|\le 2^{\omega _{1}}\)。此外，还证明了强拓扑陀螺群G的超紧p空间的性质等价于紧化中具有Lindelöf余数的G。通过这个结果，我们证明如果H是一个强拓扑陀螺群的稠密子空间G是局部伪紧而不是局部紧，那么H 的每个余数都是伪紧的。此外，如果一个强拓扑陀螺群 G有可数的伪特征并且G是不可度量的，那么G 的所有余数都是伪紧的。这两个结果部分回答了 Arhangel'skiǐ 和 Choban 提出的问题，参见（Topol Appl 157:789–799, 2010, Problem 5.1）。最后，证明了非局部紧的强拓扑陀螺群 G的 Lindelöf 性质等价于对于G 的一些紧化具有可数类型的余数。