@article{Hudson1963AFD,
title={A FINITE DIMENSIONAL HOMOGENEOUS CLAN IS A GROUP},
author={A. L. Hudson and P. Mostert},
journal={Annals of Mathematics},
year={1963},
volume={78},
pages={41}
}

A clan is a compact connected semigroup with identity. The purpose of this paper is to give a proof of the title. This gives an affirmative answer to the question of Wallace [9], and supplies the weakest algebraic conditions now extant for obtaining the compact connected (finite dimensional) groups. A space X is homogeneous if for any two points x, y E X, there is a homeomorphism qp of X onto itself such that (p(x) = y. Insofar as this result is concerned, covering, inductive, or cohomologicalâ€¦Â Expand