22. March 2013

The group of polynomial permutations modulo pn

Abstract

Fix a prime p and a positive integer n. A polynomial permutation is a bijective function over the integers modulo p^n which can be represented as a polynomial. This talk is about the group (with respect to composition) of those polynomial permutations.

While the order of the group of polynomial permutations modulo p^n is known for about a hundred years, its structure seems to be complicated. The presented results contain an enumeration of the Sylow p-subgroups and a precise description of those, and, further, some non-trivial normal subgroups will be shown.

  • This talk was given at Zahlentheoretisches Kolloquium, TU Graz, March 22, 2013.
  • categories: math, talk