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PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
 

Summary: PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 138, Number 11, November 2010, Pages 4129­4136
S 0002-9939(2010)10391-X
Article electronically published on May 27, 2010
THE TORSION INDEX OF A p-COMPACT GROUP
JAUME AGUAD´E
(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 ([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 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)

  

Source: Aguadé, Jaume - Departament de Matemàtiques, Universitat Autònoma de Barcelona

 

Collections: Mathematics