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Nilpotent block designs I: Basic concepts for Steiner triple and quadruple systems
Author(s) -
Quackenbush Robert W.
Publication year - 1999
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/(sici)1520-6610(1999)7:3<157::aid-jcd1>3.0.co;2-6
Subject(s) - fano plane , steiner system , mathematics , center (category theory) , combinatorics , block (permutation group theory) , projective plane , projective test , point (geometry) , finite geometry , nilpotent , projective geometry , element (criminal law) , set (abstract data type) , blocking set , discrete mathematics , pure mathematics , projective space , collineation , geometry , computer science , algebraic geometry , chemistry , correlation , crystallography , programming language , political science , law
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). © 1999 John Wiley & Sons, Inc. J Combin Designs 7: 157–171, 1999