Leopoldt-type theorems for non-abelian extensions of Q

Abstract

We prove new results concerning the additive Galois module structure of certain wildly ramified finite non-abelian extensions of Q. In particular, when K/Q is a Galois extension with Galois group G isomorphic to A 4 , S 4 or A 5 , we give necessary and sufficient conditions for the ring of integers O K to be free over its associated order in the rational group algebra Q[G].