REVIEW
On a permutation problem for finite abelian groups
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
On a permutation problem for finite abelian groups
read the original abstract
Let $G$ be a finite additive abelian group with exponent $n>1$, and let $a_1,\ldots,a_{n-1}\in G$. We show that there is a permutation $\sigma\in S_{n-1}$ such that all the elements $sa_{\sigma(s)}\ (s=1,\ldots,n-1)$ are nonzero if and only if $$\left|\left\{1\le s<n:\ \frac{n}{d}a_s\ne 0\right\}\right|\ge d-1\ \ \textrm{ for every positive divisor }\ d\ \textrm{ of }\ n.$$ When $G$ is the cyclic group $\mathbb Z/n\mathbb Z$, this confirms a conjecture of Z.-W. Sun.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.