Let \(G\) be the free product of two groups \(A\) and \(B\) within the class of pro-\(C\)-groups for some class \(C\) of finite groups. Sketches of proofs are given for two theorems:
Theorem 1. Any element \(g\in G\) of finite order is conjugate to some element in \(A\cup B\);
Theorem 2. \(A\) contains the centralizer in \(G\) of any of its elements \(a\neq 1\).
Theorem 2 yields an answer to a question of W. D. Geyer: a maximal abelian subgroup of the free profinite group on countably many generators can be any procyclic group \(\neq 1\).