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

Y. Fong; F. K. Huang; W. F. Ke

doi:10.1007/BF03322240

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

Y. Fong, F. K. Huang, W. F. Ke

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	53-62
Number of pages	10
Journal	Results in Mathematics
Volume	28
Issue number	1
DOIs	https://doi.org/10.1007/BF03322240
Publication status	Published - 1995 Aug

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)
Applied Mathematics

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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.",

author = "Y. Fong and Huang, {F. K.} and Ke, {W. F.}",

year = "1995",

month = aug,

doi = "10.1007/BF03322240",

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AU - Huang, F. K.

AU - Ke, W. F.

PY - 1995/8

Y1 - 1995/8

N2 - 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.

AB - 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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On Minimal Generating Sets of E(D_n), A(Dn) and I(D_n) with Even n

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