Normal subgroups of quadruply transitive permutation groups

Transitive Permutation Groups without Semiregular Subgroups

A transitive finite permutation group is called elusive if it contains no nontrivial semiregular subgroup. The purpose of the paper is to collect known information about elusive groups. The main results are recursive constructions of elusive permutation groups, using various product operations and affine group constructions. A brief historical introduction and a survey of known elusive groups a...

Permutation groups and normal subgroups

Various descending chains of subgroups of a finite permutation group can be used to define a sequence of 'basic' permutation groups that are analogues of composition factors for abstract finite groups. Primitive groups have been the traditional choice for this purpose, but some combinatorial applications require different kinds of basic groups, such as quasiprimitive groups, that are defined by...

Normal Subgroups of Triply Transitive Permutation Groups of Degree Divisible by 3

This result has been refined considerably by a number of authors. Wietandt and Huppert [14] introduced the notion of multiple primitivity and (t+ 89 transitivity. Wagner [13] showed that H is in fact t-fold transitive if n t is an even number and t > 3, and Saxl [8] proved that this is also true if t > 4 and n < 106. The only known examples of triply transitive groups with only doubly transitiv...

On Transitive Permutation Groups

We assign names and new generators to the transitive groups of degree up to 15, reflecting their structure.

Generating Transitive Permutation Groups