Abelian Projective Planes of Square Order
نویسندگان
چکیده
منابع مشابه
PROOF OF THE PRIME POWER CONJECTURE FOR PROJECTIVE PLANES OF ORDER n WITH ABELIAN COLLINEATION GROUPS OF ORDER n
Let G be an abelian collineation group of order n2 of a projective plane of order n. We show that n must be a prime power, and that the p-rank of G is at least b+ 1 if n = pb for an odd prime p.
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The generalised projectivities (GP's) associated with projective planes of odd order are investigated. These are non-singular linear mappings over GF(2) defined from the binary codes of these planes. One case that is investigated in detail corresponds to the group of an affine plane-every point corresponds to a GP. It is shown how many collineations that fix the line at infinity point-wise can ...
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We consider orthogonal arrays of strength two and even order q having n columns which are equivalent to n − 2 mutually orthogonal Latin squares of order q. We show that such structures induce graphs on n vertices, invariant up to complementation. Previous methods worked only for single Latin squares of even order and were harder to apply. If q is divisible by four the invariant graph is simple ...
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By our count, 245 projective planes of order less than 32 are currently known. This list is dominated by the 193 known planes of order 25. Most of these are either translation planes or Hughes planes, or planes obtained from these by the well-known process of repeatedly dualizing and deriving. We describe two new planes obtainable by the quite different method of ‘lifting quotients’. 2000 Mathe...
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By an unbalanced Hadamard matrix we mean a matrix H,, = (hii) such that (i) hii = l/fi or -I/fi, (ii) H, is orthogonal, and (iii) the number of positive entries exceeds the number of negative entries in each row. In particular it is well-known that the dimension n must be an even perfect square if the number of positive entries is the same in each row. It is easy to show that the number of posi...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1989
ISSN: 0195-6698
DOI: 10.1016/s0195-6698(89)80052-6