# Paper on polypermutations published!

I am pleased to announce that my latest paper, The Polypermutation Group of an Associative Ring (PDF, Journal Page) has been published with the peer-reviewed journal Contemporary Mathematics.

Briefly, this paper is a study of the group of permutations on a finite commutative ring $R$, generated by the permutations that are induced by polynomials in $R[x]$. I call it the polypermutation group of $R$. For a finite field $F$, it is easy to prove that every function $F\to F$ is of the form $a\mapsto f(a)$ where $f\in F[x]$. That is not so with all finite rings, like $\Z/4$.

In my paper, I give a presentation of this group for $\Z/p^2$ with $p$ a prime, as a semidirect product. I also derive a formula for the number of elements in this group for $\Z/p^k$ with $p\geq k\geq 2$. Although this formula is already known, I gave a new proof.

What about the journal Contemporary Mathematics? Although this journal started in 2019 and I didn’t know what to expect, the peer review process went well and the communication with the journal was excellent. As a bonus, for this particular journal, for now the publisher is waiving the open access publishing fee, so my paper is open access!