Talk:Pro-p group

canonical example?

In what sense is $\mathbb {Z} _{p}$ the canonical example? Does it satisfy a universal mapping property? --345Kai (talk) 16:53, 26 June 2017 (UTC)

I think that in this context it's meant only to indicate that it is the simplest (non-finite) example. On the other hand, I guess it also has an important role in the general theory as it is the "pro-p cyclic group" : in a pro-p group every element of infinite order topologically generates a copy of $\mathbb {Z} _{p}$. jraimbau (talk) 14:08, 27 June 2017 (UTC)