Primitive permutation groups with a sharply \(2\)-transitive subconstituent (Q1902092)

The finite uniprimitive (or simply primitive) permutation groups \(G\) which have a sharply doubly transitive subconstituent are classified in this paper. It is proved that either \(G\) has an elementary abelian normal subgroup or \(G\) is almost simple with solvable point stabilizer \(G_\alpha\) or \(G\) is isomorphic to the Baby Monster \(B\) or the Monster \(M\) and \(G_\alpha\) is a 2-local subgroup of \(G\). Of course, the classification of finite simple groups is used; the examples for the almost simple groups of non-monster type are listed explicitly.