engleski

Some Hadamard Designs with Parameters (71, 35, 17)

Up to isomorphisms there are precisely 8 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 x 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.

symmetric design; Hadamard design; orbit structure; automorphism group

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