Functions realizing as abelian group automorphisms |
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| Authors: | B-E de Klerk J Szigeti L van Wyk |
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| Institution: | 1. Department of Mathematics and Applied Mathematics, University of the Free State, Bloemfontein, South Africa;2. Department of Analysis, University of Miskolc, Miskolc, Hungary;3. Department of Mathematical Sciences, Stellenbosch University, Matieland, Stellenbosch, South Africa |
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| Abstract: | Let A be a set and f:A→A a bijective function. Necessary and sufficient conditions on f are determined which makes it possible to endow A with a binary operation ? such that (A,?) is a cyclic group and f∈Aut(A). This result is extended to all abelian groups in case |A| = p2, p a prime. Finally, in case A is countably infinite, those f for which it is possible to turn A into a group (A,?) isomorphic to ?n for some n≥1, and with f∈Aut(A), are completely characterized. |
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| Keywords: | Automorphism abelian group |
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