Cohomology and finite subgroups of profinite groups

Pham Anh Minh and Peter Symonds

Minor revision of previous version

We prove two theorems linking the cohomology of a pro-p group G with the 
conjugacy classes of its finite subgroups.

Theorem: The number of conjugacy classes of elementary abelian 
$p$-subgroups of $G$ is finite if and only if the ring H*(G,Z/p) is 
finitely generated modulo nilpotent elements.

Theorem: If the ring H*(G,Z/p) is finitely generated then the number of 
conjugacy classes of finite subgroups of $G$ is finite.