Tent, Katrin; Ziegler, Martin Sharply 2-transitive groups. (English) Zbl 1343.20002 Adv. Geom. 16, No. 1, 131-134 (2016). The finite sharply \(2\)-transitive groups were classified by H. Zassenhaus in the 1930’s, they are Frobenius groups of the form \(G=NH\) with \(N\) normal and such that \(|H|=|N|-1\). The last equality implies that in \(N\) there is a unique conjugacy class of non trivial elements and this forces \(N\) to be an elementary abelian \(p\)-group for some prime \(p\). It remained an open question whether the infinite sharply 2-transitive groups admit an abelian normal subgroup. The first counterexamples were recently constructed by E. Rips, Y. Segev and K. Tent [“A sharply 2-transitive group without a non-trivial abelian normal subgroup” arXiv:1406.0382 (2014)]; in these examples involutions have no fixed points. In the paper under review the authors give an alternative approach to such a construction by using partially defined group actions. As a corollary they prove that any group can be extended to a group acting sharply 2-transitively on some appropriate set without nontrivial abelian normal subgroup. Reviewer: Enrico Jabara (Venezia) Cited in 1 ReviewCited in 10 Documents MSC: 20B22 Multiply transitive infinite groups 20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations Keywords:infinite permutation groups; infinite sharply 2-transitive groups; Abelian normal subgroups PDFBibTeX XMLCite \textit{K. Tent} and \textit{M. Ziegler}, Adv. Geom. 16, No. 1, 131--134 (2016; Zbl 1343.20002) Full Text: DOI arXiv