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On Minimal Generating Sets of E(D n ), A(D n) and I(D n ) with Even n

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Abstract

Let Dn be the dihedral group of order 2n. Denote by E(Dn) (resp. A(Dn), I(Dn)) the distributively generated nearring generated by the set of all endomorphisms (resp. automorphisms, inner automorphisms).

In this paper, we determine for each one of the above three nearrings a minimal (additive) generating set. For E(Dn), this set contains the identity mapping and four other endomorphisms; for A(Dn), the identity mapping, one outer automorphism and one inner automorphisms; and for I(Dn), the identity mapping and two inner automorphisms.

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Authors and Affiliations

  1. Department of Mathematics, National Cheng Kung University Tainan, Taiwan, 701, Republic of China

    Y. Fong & W. F. Ke

  2. Department of Mathematics, University of Arizona, Tucson, 85721, USA

    F. K. Huang

Authors
  1. Y. Fong
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  2. F. K. Huang
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  3. W. F. Ke
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Fong, Y., Huang, F.K. & Ke, W.F. On Minimal Generating Sets of E(D n ), A(D n) and I(D n ) with Even n . Results. Math. 28, 53–62 (1995). https://doi.org/10.1007/BF03322240

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  • DOI: https://doi.org/10.1007/BF03322240

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