Pro-p Group

A pro- group, for a fixed prime , is a topological group isomorphic to an inverse limit of finite -groups. It is a profinite group whose continuous finite quotient groups all have order a power of . The additive group is an example. For a profinite group , its maximal pro- quotient is the quotient through which every continuous homomorphism from to a pro- group factors.

In the Bogomolov-Pop conjecture, a prime different from the field characteristic is fixed and the maximal pro- absolute Galois group retains field information after further passage to its abelian-by-central quotient.