✦ LIBER ✦

Nilpotent block designs I: Basic concepts for Steiner triple and quadruple systems

✍ Scribed by Robert W. Quackenbush

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 396 KB
Volume: 7
Category: Article
ISSN: 1063-8539
DOI: 10.1002/(sici)1520-6610(1999)7:3<157::aid-jcd1>3.0.co;2-6

No coin nor oath required. For personal study only.

✦ Synopsis

This paper discusses the concepts of nilpotence and the center for Steiner Triple and Quadruple Systems. The discussion is couched in the language of block designs rather than algebras. Nilpotence is closely connected to the well known doubling and tripling constructions for these designs. A sample result: a point p in an STS is projective if every triangle containing p generates the 7-element Fano plane; the p-center of the STS is the set of all projective points and is a projective geometry over GF(2).