Totally disconnected groups, p-adic groups and the Hilbert-Smith conjecture
Commun. Korean Math. Soc. 1997 Vol. 12, No. 3, 691-699
Joo Sung Lee Dongguk University
Abstract : The following statement is known as the generalized Hil- bert-Smith conjecture: If $G$ is a compact group and acts effectively on a manifold, then $G$ is a Lie group. In this paper we prove that the generalized Hilbert-Smith conjecture is equivalent to the following: A p-adic group cannot act effectively on a manifold. This fact is well known, but has never been published before.
Keywords : p-adic group, Cantor group, Lie group, non-Lie group, manifold, group action