Results 11 to 20 of about 486 (35)
Translation planes of odd order and odd dimension
International Journal of Mathematics and Mathematical Sciences, Volume 2, Issue 2, Page 187-208, 1979., 1979 The author considers one of the main problems in finite translation planes to be the identification of the abstract groups which can act as collineation groups and how those groups can act. The paper is concerned with the case where the plane is defined on a vector space of dimension 2d over GF(q), where q and d are odd.
T. G. Ostrom
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The four known biplanes with k = 11
International Journal of Mathematics and Mathematical Sciences, Volume 2, Issue 2, Page 251-260, 1979., 1979 The four known biplanes of order 9(k = 11) are described in terms of their ovals, λ‐chain structures, and automorphism groups. An exhaustive computer search for all biplanes of order 9 with certain chain structures has produced but two, one of which is new. None of these four biplanes yield the putative plane of order 10.
Chester J. Salwach, Joseph A. Mezzaroba
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International Journal of Mathematics and Mathematical Sciences, Volume 2, Issue 2, Page 261-281, 1979., 1979 Elementary techniques of algebraic coding theory are here used to discuss the three biplanes with k = 6. These three designs are intimately related to the (16, 11) extended binary Hamming code and to one another; we systematically investigate these relationships. We also exhibit each of the three designs as difference sets.
E. F. Assmus, Jr, Chester J. Salwach
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Abelian Carter subgroups in finite permutation groups
, 2013 We show that a finite permutation group containing a regular abelian self-normalizing subgroup is soluble.Comment: 6 ...
Jabara, Enrico, Spiga, Pablo
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, 2008 One of the most central and long-standing open questions in combinatorial design theory concerns the existence of Steiner t-designs for large values of t. Although in his classical 1987 paper, L.
A. Betten +40 more
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Linear spaces with significant characteristic prime
, 2006 Let $G$ be a group with socle a simple group of Lie type defined over the finite field with $q$ elements where $q$ is a power of the prime $p$. Suppose that $G$ acts transitively upon the lines of a linear space $\mathcal{S}$. We show that if $p$ is {\it
Gill, Nick
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Classification of flag-transitive Steiner quadruple systems
, 2001 A Steiner quadruple system of order v is a 3-(v,4,1) design, and will be denoted SQS(v). Using the classification of finite 2-transitive permutation groups all SQS(v) with a flag-transitive automorphism group are completely classified, thus solving the ...
Block +15 more
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, 2006 Let $N$ be a nilpotent group normal in a group $G$. Suppose that $G$ acts transitively upon the points of a finite non-Desarguesian projective plane $\mathcal{P}$.
Gill, Nick
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, 2015 We determine the automorphism group of Gabidulin codes of full length and characterise when these codes are equivalent to self-dual codes.Comment: Improved exposition according to the referees ...
Nebe, Gabriele, Willems, Wolfgang
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Existence and Classification of 3‐Regular Symmetric Graphs of Order 6pq With Distinct Primes p and q
Journal of Mathematics, Volume 2025, Issue 1, 2025.A graph Σ is said symmetric if its automorphism group acts transitively on the set of its arc. Let p < q be two distinct prime integers. This paper demonstrates that connected 3‐regular symmetric graphs of order 6pq exist if and only if the pair (p, q) belongs to the set (5, 19), (19, 37), (37, 73), which up to isomorphism there are nine sporadic ones,
Mehdi Alaeiyan +3 more
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