Transitive permutation groups of degree 𝑝=2𝑞+1, 𝑝 and 𝑞 being prime numbers. II

Abstract

Introduction. Let p be a prime number such that q = ^(p — 1) is also a prime number. Let Q be the set of symbols l,--,p, and (5 be anonsolvable transitive permutation group on O. In [10] and [11] the structure of such a permutation group © has been studied, and, in particular, the following theorem [11, Theorem 1] has been proved: If r = \(p—3) is also a prime number, then © is triply transitive. The purpose of this work is to remove this additional assumption, namely, to prove the following theorem.