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Some Hadamard designs with parameters (71,35,17)
Author(s) -
Crnković Dean,
Held Dieter
Publication year - 2002
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.996
Subject(s) - mathematics , sylow theorems , combinatorics , order (exchange) , automorphism , automorphism group , group (periodic table) , abelian group , finite group , p group , outer automorphism group , discrete mathematics , physics , finance , quantum mechanics , economics
Up to isomorphisms there are precisely eight symmetric designs with parameters (71, 35, 17) admitting a faithful action of a Frobenius group of order 21 in such a way that an element of order 3 fixes precisely 11 points. Five of these designs have 84 and three have 420 as the order of the full automorphism group G. If | G | = 420, then the structure of G is unique and we have G = (Frob 21 × Z 5): Z 4. In this case Z ( G ) = 〈1〉, G′ has order 35, and G induces an automorphism group of order 6 of Z 7. If | G | = 84, then Z ( G ) is of order 2, and in precisely one case a Sylow 2‐subgroup is elementary abelian. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 144–149, 2002; DOI 10.1002/jcd.996