Primitive normal bases for towers of field extensions

Given an extension E/F of Galois fields and an intermediate field K, we con sider the problem whether the (E, K)-trace of a primitive F-normal element of E can be a prescribed F-normal element of K. An interesting application is the existence of trace-compatible sequences of primitive F-normal elemen ts for certain towers of Galois fields. In this respect, particular emphasi s is laid on extensions having prime power degree. (C) 1999 Academic Press.