Results 1 to 10 of about 495 (36)
Forum of Mathematics, Sigma, 2023 We give a lattice theoretical interpretation of generalized deep holes of the Leech lattice VOA $V_\Lambda $ . We show that a generalized deep hole defines a ‘true’ automorphism invariant deep hole of the Leech lattice. We also show that there is a
Ching Hung Lam, Masahiko Miyamoto
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On Semisymmetric Cubic Graphs of Order 20p2, p Prime
Discussiones Mathematicae Graph Theory, 2021 A simple graph is called semisymmetric if it is regular and edge-transitive but not vertex-transitive. Let p be an arbitrary prime. Folkman proved [Regular line-symmetric graphs, J. Combin. Theory 3 (1967) 215–232] that there is no semisymmetric graph of
Shahsavaran Mohsen +1 more
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A question of Frohardt on $2$ -groups, skew translation quadrangles of even order and cyclic STGQs
Forum of Mathematics, Sigma, 2023 We solve a fundamental question posed in Frohardt’s 1988 paper [6] on finite $2$ -groups with Kantor familes, by showing that finite groups K with a Kantor family $(\mathcal {F},\mathcal {F}^*)$ having distinct members $A, B \in \mathcal
Koen Thas
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Boolean lattices in finite alternating and symmetric groups
Forum of Mathematics, Sigma, 2020 Given a group G and a subgroup H, we let $\mathcal {O}_G(H)$ denote the lattice of subgroups of G containing H. This article provides a classification of the subgroups H of G such that $\mathcal {O}_{G}(H)$ is Boolean of rank at least
Andrea Lucchini +3 more
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Pentavalent arc-transitive Cayley graphs on Frobenius groups with soluble vertex stabilizer
Open Mathematics, 2019 A Cayley graph Γ is said to be arc-transitive if its full automorphism group AutΓ is transitive on the arc set of Γ. In this paper we give a characterization of pentavalent arc-transitive Cayley graphs on a class of Frobenius groups with soluble vertex ...
Liu Hailin
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A characterization of the desarguesian planes of order q2 by SL(2, q)
International Journal of Mathematics and Mathematical Sciences, Volume 6, Issue 3, Page 605-608, 1983., 1983 The main result is that if the translation complement of a translation plane of order q2 contains a group isomorphic to SL(2, q) and if the subgroups of order q are elations (shears), then the plane is Desarguesian. This generalizes earlier work of Walker, who assumed that the kernel of the plane contained GF(q).
D. A. Foulser +2 more
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Translation planes of even order in which the dimension has only one odd factor
International Journal of Mathematics and Mathematical Sciences, Volume 3, Issue 4, Page 675-694, 1980., 1980 Let G be an irreducible subgroup of the linear translation complement of a finite translation plane of order qd where q is a power of 2. GF(q) is in the kernel and d = 2sr where r is an odd prime. A prime factor of |G| must divide . One possibility (there are no known examples) is that G has a normal subgroup W which is a W‐group for some prime W.
T. G. Ostrom
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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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