The degree and class of multiply transitive groups. III

Abstract

1. The paper to which this is a sequel had to do only with those multiply transitive groups of class ,(>3) in which at least one substitution of degree , is of even order. t Among other results, it was there proved that the degree n of triply transitive groups of class ,(>3), which contain a substitution of even order on , letters, does not exceed 2,. Triply transitive groups of class A and degree 2, exist. This measure of success was due to the simplicity of structure of diedral rotation groups of class , generated by two similar substitutions of degree , and order 2. Up to the present time no better limit than that of Bochert, n_3,u(,u>6), has been found to apply to these triply transitive groups of class , >3) in which all substitutions of degree , are of odd order. t But it will here be proved that if such a group contains a substitution of order pc (p an odd prime) on , letters,