Computing Class Groups With an Inductive Algorithm

In this talk, first, I will present a method by Biasse, Fieker, Hoffman and Page to compute the class group of some number fields inductively. This method uses the properties of norm relations, which are some relations in R[G] where R is a commutative ring and G a finite group. Then, I will discuss about how we can generalise the notion of norm relations and use this new kind of relations to obtain a similar method for computing class groups, that is more effective than the previous one.