Construction of block designs admitting an Abelian automorphism group

Abstract

Construction of block designs admitting an action of a presumed automorphism group consists of two basic steps:

1.construction of orbit structures for the given automorphism group,

2. construction of block designs for the orbit structures obtained in 1.

For an abelian group G, the second step, called indexing, often lasts too long, because there are too many possibilities to be enumerated with today's computer facilities. To make such a construction possible we use a principal series of the group G to obtain a refinement of the orbit structures.