Commutative Subgroups and Torsion in Compact Lie Groups

In this note, G is a compact connected Lie group. We are concerned with the torsion of the cohomology ring H*(G; Z) of G over the integers, certain commutative subgroups of G, and relations between these two questions. NOTATION. E(mi, • • • , mr) or £ A ( ^ I , • • • , mr) denotes the exterior algebra over the ring A of a free .4-module with r generators of respective degrees wi, • • • , mr; p is a prime number, Zv the field of integers mod p1 Q the field of rational numbers. Tors H is the torsion subgroup of a group Hy ord M the order of a finite group M. The identity component of a closed subgroup H if G is denoted by Ho, if L is a subset of G, its centralizer in G is denoted by Z(L).