An extension of building sets and relative difference sets

Building sets are a successful tool for constructing semi-regular divisible difference sets and, in particular, semi-regular relative difference sets, In this paper, we present an extension theorem for building sets under simple conditions, Some of the semi-regular relative difference sets obtained using the extension theorem are new in the sense that their ambient groups have smaller ranks than previously known. (C) 2000 John Wiley & Sons, Inc.