 
Summary: PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 138, Number 11, November 2010, Pages 41294136
S 00029939(2010)10391X
Article electronically published on May 27, 2010
THE TORSION INDEX OF A pCOMPACT GROUP
JAUME AGUAD´E
(Communicated by Brooke Shipley)
Abstract. We extend the theory of torsion indices of compact connected Lie
groups to pcompact 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 ([10]) and has been investigated by several authors ([14], [6], [15], etc.).
Recently, the computation of the torsion indices of all simply connected compact
Lie groups has been completed (see [16]). 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 padic 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)
