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Symmetric Words in Dihedral Groups
Algebra Colloquium, 2010Let G be a group and let w = w(x1, x2,…, xn) be a word in the absolutely free group Fnon free variables x1, x2,…, xn. The set S(n)(G) of all words w such that the equality w(gσ1, gσ2,…, gσn) = w(g1, g2,…, gn) holds for all g1, g2,…, gn∈G and all permutations σ ∈ Snis a subgroup of Fn, called the subgroup of n-symmetric words for G.
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Hadamard Matrices and Dihedral Groups
Designs, Codes and Cryptography, 1996An \(n\times n\) matrix with elements \(0\) and \(1\) is called an Hadamard matrix, if the matrix \(H\) obtained from it by changing \(0\)'s to \(-1\)'s satisfies \(HH'=nI_n\). Let \(\text{D}_{2p}\) be a dihedral group of order \(2p\), where \(p\) is an odd integer and \(\mathbb{Z}\text{D}_{2p}\) be the group ring of \(\text{D}_{2p}\) over the ring ...
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Journal of Information and Optimization Sciences, 2018
In this paper we consider the group algebra FG, where characterstic of the field F does not divide order the group G, then FG is semisimple, and hence decomposes into a direct sum of minimal ideals generated by the idempotents .We give the explicit expressions for the idempotents in the group algebra of dihedral group of order 2n for every n.
Sudesh Sehrawat, Manju Pruthi
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In this paper we consider the group algebra FG, where characterstic of the field F does not divide order the group G, then FG is semisimple, and hence decomposes into a direct sum of minimal ideals generated by the idempotents .We give the explicit expressions for the idempotents in the group algebra of dihedral group of order 2n for every n.
Sudesh Sehrawat, Manju Pruthi
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2017
The aim of this chapter is to describe the Kazhdan–Lusztig basis, the different partitions into cells, as well as the structure of the cell modules for all choices of parameters. The first important consequence is the construction of left, right and two-sided cellular maps (which were used in Chapters 9 and 12).
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The aim of this chapter is to describe the Kazhdan–Lusztig basis, the different partitions into cells, as well as the structure of the cell modules for all choices of parameters. The first important consequence is the construction of left, right and two-sided cellular maps (which were used in Chapters 9 and 12).
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Group Rings of Dihedral Groups
2012In this chapter we continue the study of stably free cancellation over the integral group rings Z[F n ×Φ] in the case where Φ is the dihedral group of order 2m defined by the presentation $$D_{2m} = \langle x, y \vert x^m = y^2 = 1 , yx = x^{m-1}y \rangle.$$ Our main result, first proved in Johnson (Q. J. Math., 2011, doi: 10.1093/qmath/har006),
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The infinite dihedral group as automorphism group.
2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
F. DE GIOVANNI, RUSSO, Alessio
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Cancer statistics for adolescents and young adults, 2020
Ca-A Cancer Journal for Clinicians, 2020Kimberly D Miller +2 more
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