Frattini injective pro-$p$ groups

Abstract: A pro-p group $G$ is said to be Frattini-injective if distinct finitely generated subgroups of $G$ have distinct Frattinis. Examples of Frattini-injective groups are provided by the maximal pro-$p$ Galois groups of fields that contain a primitive $p$th root of unity. I will discuss a joint work with Ilir Snopche in which we make a first attempt to systematically study Frattini-injectivity.

group theoryrings and algebras

Audience: researchers in the topic

( paper )

Al@Bicocca take-away