Some remarks on conjectures about cyclotomic fields and -groups of
Let p be a rational prime, G a group of order p, and K a number field containing a primitive pth root of unity. We show that every tamely ramified Galois extension of K with Galois group isomorphic to G has a normal integral basis if and only if for every Galois extension L/K with Galois group isomorphic to G, the ring of integers in L is free as a module over the associated order . We also give examples, some of which show that this result can still hold without the assumption that K contains...