On cyclic semi-regular subgroups of certain 2-transitive permutation groups

A note on cyclic semiregular subgroups of some 2-transitive permutation groups

We determine the semi-regular subgroups of the 2-transitive permutation groups PGL(2, n),PSL(2, n),PGU(3, n),PSU(3, n),Sz(n) and Ree(n) with n a suitable power of a prime number p. 2000 Math. Subj. Class.: 14H37

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...

On Transitive Permutation Groups

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

Permutation Groups with a Cyclic Regular Subgroup and Arc Transitive Circulants

A description is given of finite permutation groups containing a cyclic regular subgroup. It is then applied to derive a classification of arc transitive circulants, completing the work dating from 1970’s. It is shown that a connected arc transitive circulant of order n is one of the following: a complete graph Kn , a lexicographic product [K̄b], a deleted lexicographic product [K̄b] − b , where ...

Generating Transitive Permutation Groups