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Functions realising as abelian group automorphisms. (arXiv:1810.07533v1 [math.GR])
来源于:arXiv
Let $A$ be a set and $f:A\rightarrow A$ 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 $f\in
\mbox{Aut}(A)$. This result is extended to all abelian groups in case $|A|=p^2,
\ p$ 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 ${\Bbb Z}^n$ for
some $n\ge 1$, and with $f\in \mbox{Aut} (A)$, are completely characterised. 查看全文>>