A profinite group is a topological group isomorphic to an inverse limit of finite
discrete groups. Equivalently, it is a compact Hausdorff totally disconnected topological group. Its open normal
subgroups give finite quotient groups, and these quotients
determine the topology. For example, the additive group
of 
-adic
integers is the inverse limit of 
. A pro-p group
is an inverse limit of finite
groups of prime-power order 
for a fixed prime 
.
Absolute Galois groups are profinite. The maximal pro-
quotient and its abelian-by-central quotient occur in the Bogomolov-Pop
conjecture.
