Fixed-point-free 2-finite automorphism groups.
A group \(G\) is called \(n\)-finite if any \(n\) elements of \(G\) generate a finite subgroup. The main result of the paper states that a fixed-point-free group \(G\) of automorphisms of an Abelian \(2\)-finite group is locally finite. Earlier \textit{A. I. Sozutov} [in Sib. Math. J. 35, No. 4, 795-801 (1994); translation from Sib. Mat. Zh. 35, No. 4, 893-901 (1994; Zbl 0851.20039)] characterized the subgroups of \(G\) generated by all elements of prime order. The main theorem implies that a nearfield with \(2\)-finite multiplicative group is a locally finite nearfield, and a sharply \(2\)-transitive \(2\)-finite permutation group is locally finite.
scientific article; zbMATH DE number 5963406