Soundararajan, T. Groups of automorphisms of algebraically closed extension fields. (English) Zbl 0531.12020 Math. Today 1, 17-24 (1983). If E is an algebraically closed field of prime characteristic p, then the Frobenius automorphism f, which maps each element to its p-th power, lies in the center of the group Aut E of all automorphisms of E. Moreover, if F is a subfield of E such that E is not an algebraic extension of F, then the author proves that the center of Aut E is the infinite cyclic group \(<f>\) generated by f and the center of the group G of automorphisms of E over F is \(G\cap<f>\). Thus the center of G is nontrivial if and only if F is a finite field. The proofs are detailed and straightforward. The author also makes some elementary observations about the structure of G with respect to the Krull topology. Reviewer: H.F.Kreimer MSC: 12F20 Transcendental field extensions 20B27 Infinite automorphism groups Keywords:automorphism of field; Frobenius automorphism; Krull topology PDFBibTeX XMLCite \textit{T. Soundararajan}, Math. Today 1, 17--24 (1983; Zbl 0531.12020)