Summary: PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 138, Number 11, November 2010, Pages 41294136
Article electronically published on May 27, 2010
THE TORSION INDEX OF A p-COMPACT GROUP
(Communicated by Brooke Shipley)
Abstract. We extend the theory of torsion indices of compact connected Lie
groups to p-compact groups and compute these indices in all cases.
1. Introduction and statement of results
The torsion index of a compact connected Lie group was defined by Grothendieck
in 1958 () and has been investigated by several authors (, , , etc.).
Recently, the computation of the torsion indices of all simply connected compact
Lie groups has been completed (see ). Since we are going to work at a single
prime p, instead of the torsion index of a Lie group G, we want to consider its p-
primary part tp(G). We summarize the properties of tp(G) which are relevant to the
present work in the following proposition (Zp denotes the ring of p-adic integers).
Theorem 1.1. Let p be a prime and let G be a compact connected Lie group with
a maximal torus T and corresponding Weyl group W. The positive integer tp(G)