Automorphism towers and automorphism groups of fields without Choice

Details Automorphism towers and automorphism groups of fields without Choice Automorphism towers and automorphism groups of fields without Choice

2010-04-11

arxiv.org/abs/1004.1810v5

Mathematics

Logic

Scientific paper

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.

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