  This paper can be viewed as a continuation of [KS09] that dealt with the
automorphism tower problem without Choice. Here we deal with the inequation
which connects the automorphism tower and the normalizer tower without Choice
and introduce a new proof to a theorem of Fried and Koll\'ar that any group can
be represented as an automorphism group of a field. The proof uses a simple
construction: working more in graph theory, and less in algebra.
