2-transitive symmetric designs

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University of Wisconsin--Madison, 1968 - Mathematics - 202 pages
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Background and Preliminary Results
Automorphism Groups of Designs

8 other sections not shown

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2-homogeneous 2-transitive automorphism group 2-transitive collineation group 2-transitive group 2-transitive symmetric design 4—transitive abelian group abelian subgroup acts faithfully admits a 2-transitive admitting an automorphism affine space assume automor BflX block X block-orbits blocks of D blocks on q Burnside Burnside's theorem complementary design contains the little contradiction Corollary 8.2 D admits Dembowski design D design of points difference set design distinct blocks distinct points dual dually elementary abelian every block finite field finite protective space fixed points fixes a point fixing a block flag-transitive following result four points Frobenius group full automorphism group group of D group of degree Hadamard design However hyperplanes implies imprimitivity classes incidence structure integer intransitive subgroup involution isomorphic Lemma Lemma 3.5vii length v-k Let D little protective group minimal normal subgroup morphism non-trivial normal subgroup number of points orbit of length orbit of TT orbits of ordered ordered pairs pair of points parameters PB is 2-transitive permutation group phism group point-orbits points and blocks points of CB pointwise polarity polynomials prime divisor prime power primitive proof of Theorem proper divisor Proposition proves relatively prime remaining blocks resp Ryser sharply sharply transitive sibility Since sitive space or H square-free stabilizer subdesign subgroup Z Suppose Sylow 2-subgroup symmetric design admitting system of imprimitivity system of k/c Theorem 3.1 Thus transitive and regular transitive on CB TT of blocks University of Wisconsin usual representation v-l)/k an integer Wagner Wielandt Z fixes Zassenhaus

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