Simple groups with prescribed local structure. (Q624860)

In this paper the author constructs simple groups of certain types. In particular let \(\mathcal B\) be a variety in which the free groups of infinite rank are residually finite. The author shows that for every cardinal \(\kappa\) there exists a locally (\(\mathcal B\)-by-finite) simple group \(S(\kappa)\) of cardinality equal to \(\max\{\kappa,\aleph_0\}\) which contains a copy of the \(\mathcal B\)-free group of rank \(\kappa\). This generalizes a theorem of \textit{M. R. Dixon, M. J. Evans} and \textit{H. Smith} [J. Group Theory 12, No. 5, 745-752 (2009; Zbl 1192.20017)]. This is a very nice paper.