Characterisations of \(A_{p+2}\) and \(L_ 2(2^ q)\)
Finite transitive permutation groups of degree \(p+2\) are considered which contain a cycle of prime length \(p\geq 5\). (Clearly, such a group is triply-transitive, and it is easily shown that the unique minimal normal subgroup \(N\) of \(G\) is also triply-transitive.) Based on the fact that a simple triply-transitive group of degree \(p+2\) is either permutation isomorphic to the alternating group \(A_{p+2}\) or to \(L_2(2^q)\) in its natural representation of degree \(2^q+1\) where \(p=2^q-1\), all these groups are classified. -- The fact mentioned is not proved in the paper, but it follows from the classification of finite simple groups.
scientific article; zbMATH DE number 1028208