Results 11 to 20 of about 96 (96)
Discrete Mathematics, 2005 The authors give a very readable description of the history of generalized quadrangles which satisfy the Moufang condition, or some weaker condition, up to 2003. Moreover, they classify all finite thick generalized quadrangles which are quasi-transitive (this is a natural transitivity condition for generalized homologies).
Koen Thas, Hendrik Van Maldeghem
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A weak Moufang condition suffices
European Journal of Combinatorics, 2005 The 2-Moufang condition for generalized polygons states that for any point or line \(x\), the stabilizer of all elements incident with \(x\) acts transitively on the elements opposite \(x\). Moufang polygons are automatically 2-Moufang. The question is, whether the 2-Moufang condition implies the Moufang condition.
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The commutative Moufang loops with maximum conditions for subloops
, 2008 10 ...
Babiy, A., Sandu, N.
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On some criterions of finiteness conditions in commutative Moufang loops
, 2008 The various finiteness conditions in commutative Moufang loops are characterized using the notions of centralizer of subloops and centralizer of subgroups of its multiplication group.
Babiy, Aliona, Sandu, Nicolae
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Topological Aspects of Quadratic Graphs and M‐Polynomials Utilizing Classes of Finite Quasigroups
Journal of Mathematics, Volume 2026, Issue 1, 2026.Material science, drug design and toxicology studies, which relate a molecule’s structure to its numerous properties and activities, are studied with the use of the topological index. Graphs with finite algebraic structure find extensive applications in fields such as mathematics, elliptic curve cryptography, physics, robotics and information theory ...
Mohammad Mazyad Hazzazi +5 more
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Commuting Pairs in Quasigroups
Journal of Combinatorial Designs, Volume 33, Issue 11, Page 418-427, November 2025.ABSTRACT A quasigroup is a pair ( Q , ∗ ), where Q is a nonempty set and ∗ is a binary operation on Q such that for every ( a , b ) ∈ Q 2, there exists a unique ( x , y ) ∈ Q 2 such that a ∗ x = b = y ∗ a. Let ( Q , ∗ ) be a quasigroup. A pair ( x , y ) ∈ Q 2 is a commuting pair of ( Q , ∗ ) if x ∗ y = y ∗ x.
Jack Allsop, Ian M. Wanless
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Strong transitivity, Moufang's condition and the Howe--Moore property
, 2020 Firstly, we prove that every closed subgroup $H$ of type-preserving automorphisms of a locally finite thick affine building $Δ$ of dimension $\geq 2$ that acts strongly transitively on $Δ$ is Moufang. If moreover $Δ$ is irreducible and $H$ is topologically simple, we show that $H$ is the subgroup $\G(k)^+$ of the $k$-rational points $\G(k)$ of the ...
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Extensions of Steiner Triple Systems
Journal of Combinatorial Designs, Volume 33, Issue 3, Page 94-108, March 2025.ABSTRACT In this article, we study extensions of Steiner triple systems by means of the associated Steiner loops. We recognize that the set of Veblen points of a Steiner triple system corresponds to the center of the Steiner loop. We investigate extensions of Steiner loops, focusing in particular on the case of Schreier extensions, which provide a ...
Giovanni Falcone +2 more
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Linking Bipartiteness and Inversion in Algebra via Graph‐Theoretic Methods and Simulink
Complexity, Volume 2025, Issue 1, 2025.Research for decades has concentrated on graphs of algebraic structures, which integrate algebra and combinatorics in an innovative way. The goal of this study is to characterize specific aspects of bipartite and inverse graphs that are associated with specific algebraic structures, such as weak inverse property quasigroups and their isotopes ...
Mohammad Mazyad Hazzazi +6 more
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On the Menelaus and Ceva 6‐Figures in the Fibered Projective Planes
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 The fibered versions of Menelaus and Ceva 6‐figures in the fibered projective plane are given and the conditions to the fibered versions of Menelaus and Ceva 6‐figures in the fibered projective plane with base plane, that is, projective plane, are determined.
Ayşe Bayar +2 more
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