188
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Functions realizing as abelian group automorphisms

, , &
Pages 467-479 | Received 02 Sep 2015, Published online: 06 Nov 2017
 

ABSTRACT

Let A be a set and f:AA 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.

2010 MATHEMATICS SUBJECT CLASSIFICATION:

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.

Log in via your institution

Log in to Taylor & Francis Online

PDF download + Online access

  • 48 hours access to article PDF & online version
  • Article PDF can be downloaded
  • Article PDF can be printed
USD 61.00 Add to cart

Issue Purchase

  • 30 days online access to complete issue
  • Article PDFs can be downloaded
  • Article PDFs can be printed
USD 1,187.00 Add to cart

* Local tax will be added as applicable

Related Research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.