The structure of 3-pyramidal groups.

A combinatorial block design D is called f -pyramidal if there exists a subgroup G of Aut (D) fixing f points and acting regularly on the other points. If this happens, we say that the design is f -pyramidal under G. In case D is a 3-pyramidal Kirkman triple system, it is known that such a group G has precisely 3 involutions, all conjugate to each other. In this paper, we obtain a classification of the groups with this property. [ABSTRACT FROM AUTHOR]