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Some Hadamard designs with parameters (71,35,17)

✍ Scribed by Dean Crnković; Dieter Held

Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
106 KB
Volume
10
Category
Article
ISSN
1063-8539

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✦ Synopsis

Abstract

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

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