All 2-transitive groups have the EKR-module property

Sharply 2-transitive groups

We give an explicit construction of sharply 2-transitive groups with fixed point free involutions and without nontrivial abelian normal subgroup.

Divergence Groups Have the Bowen Property

Moore groups have the WS-property

All groups of odd order have starter-translate 2-sequencings

Bailey defined 2-sequencings (terraces) of groups. She conjectured that all finite groups except elementary Abelian 2-groups (other than the cyclic group Z2) have 2-sequencings and proved that the direct product of a 2-sequenceable group and a cyclic group of odd order is 2-sequenceable. It is shown here that all groups of odd order have a special type of 2-sequencing called a starter-translate...

All vertex-transitive locally-quasiprimitive graphs have a semiregular automorphism

The polycirculant conjecture states that every transitive 2-closed permutation group of degree at least two contains a nonidentity semiregular element, that is, a nontrivial permutation whose cycles all have the same length. This would imply that every vertex-transitive digraph with at least two vertices has a nonidentity semiregular automorphism. In this paper we make substantial progress on t...