On the elation structure of specific designs

Consider symmetric 2-designs D which have an automorphism group G containing sufficiently many elations. This paper proves that all elations in G have the same order and classifies the elation structure (i.e. centre-axis pairs) of a well-defined subgroup of G. For one class, D is necessarily a projective space.The results in this paper form part of a PhD thesis submitted by the author to the University of London. The author gratefully acknowledges the support of the Commonwealth Scholarship Commission.