Turkish Journal of Mathematics
Abstract
For a given positive integer $n$, the structure, i.e. the number of cycles of various lengths, as well as possible chains, of the automorphisms of the groups $(\Z^n, +)$ and $(\Z_p^n,+)$, \ $p$ prime, is studied. In other words, necessary and sufficient conditions on a bijection $f : A \ra A$, where $ A $ is countably infinite (alternatively, of order $p^n$), are determined so that $A$ can be endowed with a binary operation $*$ such that $(A,*)$ is a group isomorphic to $(\Z^n,+)$ (alternatively, $(\Z_p^n,+)$) and such that $f\in \Aut(A)$.
DOI
10.3906/mat-1805-84
Keywords
Automorphism, abelian group
First Page
2965
Last Page
2978
Recommended Citation
KLERK, B. D, & MEYER, J. H (2018). When is a permutation of the set $\Z^n$ (resp. $\Z_p^n$, $p$ prime) an automorphism of the group $\Z^n$ (resp. $\Z_p^n$)?. Turkish Journal of Mathematics 42 (6): 2965-2978. https://doi.org/10.3906/mat-1805-84
