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Let p be an odd prime number and let K be an imaginary quadratic number field whose class number is not divisible by p. For a set S of primes of K whose norm is congruent to 1 modulo p, we introduce the notion of strict circularity. We show that if S is strictly circular, then the group G(KS(p)/K) is of cohomological dimension 2 and give some explicit… (More)
We announce the creation of a database of invariant rings. This database contains a large number of invariant rings of finite groups, mostly in the modular case. It gives information on generators and structural properties of the invariant rings. The main purpose is to provide a tool for researchers in invariant theory.
Let p be an odd prime number, k a number field and S a set of primes of k containing some, but not all primes of k above p. We study under which conditions GS(k)(p) is a mild pro-p-group of deficiency one, and apply our results to the case of imaginary quadratic number fields.
We give effective necessary and sufficient conditions for a quadratically defined 2-relator prop group to be mild and apply these results to give examples of 2-extensions with restricted ramification over an imaginary quadratic base field for which the associated Galois group is a mild 2-relator pro-2-group. Contents 1. Introduction 281 2. Computation of… (More)