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 ℤn for some n≥1, and with f∈Aut(A), are completely characterized.
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Acknowledgments
The first, second and fourth authors would like to thank the National Research Foundation of South Africa for financial assistance. All the authors would also like to thank the referees for valuable comments and suggestions.