Title:  Frattini-resistance and maximal pro-p Galois groups

Abstract: Given a pro-p group G,  let Φ(G) be the Frattini subgroup of G.  We call a pro-p group G Frattini-resistant if for all finitely generated subgroups H and K of G,  Φ(H) ≤ Φ(K) implies H ≤ K. 

I will talk about Frattini-resistant pro-p groups and their relation with maximal pro-p Galois groups.

This is a joint work with Slobodan Tanushevski.