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Symmetric designs with parameters (69, 17, 4) and F 39 as a group of automorphisms
Author(s) -
Boz˘ikov Zdravka
Publication year - 1998
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(1998)6:4<231::aid-jcd1>3.0.co;2-g
Subject(s) - mathematics , automorphism , converse , combinatorics , invariant (physics) , combinatorial design , symmetric group , group (periodic table) , automorphisms of the symmetric and alternating groups , order (exchange) , pure mathematics , chemistry , geometry , organic chemistry , finance , economics , mathematical physics
According to Mathon and Rosa [ The CRC handbook of combinatorial designs , CRC Press, 1996] there is only one known symmetric design with parameters (69, 17, 4). This known design is given in Beth, Jungnickel, and Lenz [ Design theory , B. I. Mannheim, 1985]; the Frobenius group F 39 of order 39 acts on this design, where Z 13 has exactly 4 fixed points and Z 3 has exactly 9 fixed points. The purpose of this article is to investigate the converse of this fact with the hope of obtaining in this way at least one more design with these parameters. In fact we obtain exactly one new such design. In this article we have classified all such designs invariant under F 39 . © 1998 John Wiley & Sons, Inc. J Combin Designs 6: 231–233, 1998