Centers and Coxeter elements
W. G. Dwyer and C. W. Wilkerson

Abstract:
Suppose that $G$ is a connected compact Lie group. We show that
simple numerical information about the Weyl group of $G$ can be used
to obtain bounds, often sharp, on the size of the center of $G$.
These bounds are obtained with the help of certain Coxeter elements
in the Weyl group. Variants of the method use generalized Coxeter
elements and apply to $p$-compact groups; in this case a splitting theorem
emerges. The Lie group results are mostly known, but our arguments
have a conceptual appeal.