On the Fundamental Group of a Homegeneous Space

摘要

In this paper, it is proved that more generally if the fundamental group of a homogeneous space (see §3 for definition) M is solvable, then it is finitely generated and its rank cannot exceed the dimension of M. Our method consists of reducing to the case in which the group acting transitively on the homogeneous space is itself solvable and then applying results of the author on solvable Lie groups.