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Syntactic Nearrings

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Part of the Mathematics and Its Applications book series (MAIA, volume 336)

Abstract

Let G be a finite group written additively and S = (G, G, δ) a group semiautomaton. In this paper we investigate the subnearring N (σ, τ) (S) of M(G), referred to as the syntactic nearring of S, with δ(x,y) = xσ + yτ for σ, τ, ∈ M(G). By definition, N(σ, τ)(S) is the subnearring of M(G) generated by under pointwise addition and composition of mappings. We first prove the key result that if (G,+) is a finite group, σ ∈ M(G) and m, n ∈ Z, then. Finally, we apply the result to the case where G = S3, the symmetric group of degree 3, and give a detailed study for the case S = (S3, S3, δ) with δ(x,y) = mx + ny for various syntactic nearrings.

Keywords

Normal Subgroup Transition Function Finite Group Symmetric Group Dihedral Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  1. 1.Department of MathematicsNational Cheng Kung UniversityTainanTaiwan, R. O. C
  2. 2.Department of MathematicsChinese Air Force AcademyKang SanTaiwan, R. O. C.

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