Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8895717 | Finite Fields and Their Applications | 2018 | 14 Pages |
Abstract
Let PPol(R) denote the group of permutation polynomial functions over the finite, commutative, unital ring R under composition. We generalize numerous results about permutation polynomials over Zpn to local rings by treating them under a unified manner. In particular, we provide a natural wreath product decomposition of permutation polynomial functions over the maximal ideal M and over the finite field R/M. We characterize the group of permutation polynomial functions over M whenever the condition M|R/M|={0} applies. Then we derive the size of PPol(R), thereby generalizing the same size formulas for Zpn. Finally, we completely characterize when the group PPol(R) is solvable, nilpotent, or abelian.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Dalma Görcsös, Gábor Horváth, Anett Mészáros,