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RESEARCH PRODUCT
Some Hadamard designs with parameters (71,35,17)
Dean CrnkovićDieter Heldsubject
Combinatoricssymmetric design; Hadamard design; orbit structure; automorphism groupInner automorphismSylow theoremsStructure (category theory)Discrete Mathematics and CombinatoricsOuter automorphism groupOrder (group theory)Abelian groupElement (category theory)Frobenius groupMathematicsdescription
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 = (Frob21 × Z5):Z4. In this case Z(G) = 〈1〉, G′ has order 35, and G induces an automorphism group of order 6 of Z7. 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
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2002-01-01 | Journal of Combinatorial Designs |