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On divisible designs and local algebras
Author(s) -
Spera Antonino Giorgio
Publication year - 1995
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/jcd.3180030307
Subject(s) - mathematics , commutative property , dimension (graph theory) , class (philosophy) , projective space , projective test , order (exchange) , action (physics) , combinatorics , pure mathematics , field (mathematics) , construct (python library) , space (punctuation) , discrete mathematics , algebra over a field , computer science , physics , finance , quantum mechanics , artificial intelligence , economics , programming language , operating system
We study the action of the group PGL( m,A ) on the projective space PG( m − 1, A ) over a finite commutative local algebra A in order to construct a class of divisible designs, denoted by D m (d,A) , which is the classical one of 2‐designs (of points and of flats of fixed projective dimension) in the case where A is a field. We also study the constructed divisible designs with particular care for the case where d = m − 1. © 1995 John Wiley & Sons, Inc.