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Weak Cayley tables and generalized centralizer rings of finite groups
Mathematical Proceedings of the Cambridge Philosophical Society, 2012AbstractFor a finite groupGwe study certain rings(k)Gcalledk-S-rings, one for eachk≥ 1, where(1)Gis the centraliser ringZ(ℂG) ofG. These rings have the property that(k+1)Gdetermines(k)Gfor allk≥ 1. We study the relationship of(2)Gwith the weak Cayley table ofG.
Humphries, Stephen P., Rode, Emma L.
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On the category of weak Cayley table morphisms between groups
Selecta Mathematica, 2007Weak Cayley table functions between groups are generalized conjugacy-preserving homomorphisms, under which products of images are conjugate to images of products. There is a weak Cayley table bijection between two groups iff they have the same 2-characters.
K. W. Johnson, J. D. H. Smith
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Gradient based fractal image compression using Cayley table
Measurement, 2019Abstract Encoding complexity reduction is an active area of research in the field of fractal image compression. In this proposed method, affine transformation is predicted to reduce the computational complexity and score value is calculated to further minimise the number of computations in the exhaustive process of encoding.
K. Sheeba, M. Abdul Rahiman
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An algorithm for Cayley tables of algebras
Zbornik radova Prirodno-matematičkog fakulteta u Novom Sadu, serija Matematika, 1993This paper presents an algorithm to determine all nonisomorphic semigroups of \(n\) elements. The authors consider three types of elements: freely defined elements, defined elements and undefined elements, and make each element of the matrix of the Cayley table correspond to an ordinal number.
Crvenković, Siniša, Stojmenović, Ivan
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The Cayley Addition Table of Z n
The American Mathematical Monthly, 1999(1999). The Cayley Addition Table of Zn. The American Mathematical Monthly: Vol. 106, No. 6, pp. 584-585.
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On the spectrum of Cayley graphs via character table
2014A Cayley graph can be consider as an interpretation of group representation. This means that one can construct the Cayley graph Г = Cay(G, S) by having the vertex set to be the elements of G with g~h if and only if hg-1 e S. In this paper, we focus our attention on Cayley graphs with a normal symmetric subset.
Nowroozi, Farzaneh, Ghorbani, Modjtaba
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Weak Cayley Table Groups II: Alternating Groups and Finite Coxeter Groups
Communications in Algebra, 2015A weak Cayley table isomorphism is a bijection φ: G → H of groups such that φ(xy) ∼ φ(x)φ(y) for all x, y ∈ G. Here ∼denotes conjugacy. When G = H the set of all weak Cayley table isomorphisms φ: G → G forms a group 𝒲(G) that contains the automorphism group Aut(G) and the inverse map I: G → G, x → x −1.
Stephen P. Humphries, Long Nguyen
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Weak Cayley table groups III:PSL(2,q)
Communications in Algebra, 2016ABSTRACTA weak Cayley table isomorphism is a bijection φ:G→H of groups such that φ(xy)∼φ(x)φ(y) for all x,y∈G. Here ∼ denotes conjugacy. When G = H the set of all weak Cayley table isomorphisms φ:G→G forms a group 𝒲(G) that contains the automorphism group Aut(G) and the inverse map I:G→G,x↦x−1.
Stephen P. Humphries, Long Nguyen
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Visualizing large-order groups with computer-generated Cayley tables
Journal of Mathematics and the Arts, 2017ABSTRACTLarge-order finite groups have been made the subject of artwork through abstract computer-generated pictures corresponding to Cayley tables which have been presented in some recent mathematical art exhibits and galleries. In our present article, we further explore the concept of using computer art to visualize large-order groups, by offering ...
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Optimal Constructions of LRCs based on Cayley Table
2023 14th International Conference on Computing Communication and Networking Technologies (ICCCNT), 2023Deep Mukhopadhyay +3 more
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