Speaker: Sela Fried (Tel-Aviv University): Title: Quasi-formations of finite groups Abstract: We define quasi-formations that generalize formations of finite groups and show that for every quasi-formation C there exists an (up to an isomorphism) unique pro-C group of at most countable rank with the embedding property, that has C as its class of finite images. This group is an analogue of a free pro-C group. We will apply our theory to the absolute Galois group of the maximal pro-solvable extension of Q under the assumption that Shafarevich conjecture is valid, namely that the absolute Galois group of the maximal abelian extension of Q is the free profinite group on a countable set. The content of the lecture is part of my dissertation written under the supervision of Dan Haran.