A permutability problem in infinite groups and Ramsey's theorem (Q2748264)

This paper belongs to the long series of papers that derive properties of a group from assumptions on one or more infinite sets of elements of the group. The authors begin by generalizing the definitions of Sidon sets of \textit{L. Babai} and \textit{V. T. Sós} [in Eur. J. Comb. 6, 101-114 (1985; Zbl 0573.05032)], and go on to generalize one of the propositions in the Babai and Sós paper. As is natural in this kind of group theory, the authors apply Ramsey's well-known 1929 theorem in the proof. The details of the definitions and results are too technical to reproduce here.