Extensions of Homomorphisms and the Structure of Ray Class Groups Original Research Article

We study group extensions associated to the ray class groups arising in class field theory. This involves a new kind of Ext-group classifying extensions of a homomorphism by a group. It is shown that, when applied to our arithmetic situation, a description of the extension structure is obtained in terms of the splitting behaviour of primes dividing the conductor of the ray class group in certain explicit field extensions. This gives rise to various density statements telling us how often a certain group extension will occur.