On minimal generating sets of \(E(D_ n)\), \(A(D_ n)\) and \(I(D_ n)\) with even \(n\) (Q1896648)
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scientific article; zbMATH DE number 792556
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On minimal generating sets of \(E(D_ n)\), \(A(D_ n)\) and \(I(D_ n)\) with even \(n\) |
scientific article; zbMATH DE number 792556 |
Statements
On minimal generating sets of \(E(D_ n)\), \(A(D_ n)\) and \(I(D_ n)\) with even \(n\) (English)
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30 January 1996
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If \(G\) is a group, then \(I(G)\) and \(A(G)\) are the near-rings generated by all inner and all automorphisms of \(G\) while \(E(G)\) is the near-ring generated by the endomorphisms of \(G\). \textit{C. G. Lyons} and \textit{J. J. Malone} [Compos. Math. 24, 305-312 (1972; Zbl 0236.16027); 26, 249-259 (1973; Zbl 0266.16034)] studied the three near-rings when \(G\) is a finite dihedral group. In the paper under review the authors find minimal additive generating sets for them.
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minimal generating sets
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near-rings
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automorphisms
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endomorphisms
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finite dihedral groups
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