Discrete Functions

Research of the group of bijective differentiable modulo $p^n$ functions

A. S. Ivachev

Tomsk State University, Tomsk

Abstract: The group of bijective differentiable modulo $p^n$ functions is researched up to isomorphism. A method of searching for conjugation element in this group is proposed. The method consists in solving a system of linear equations over $\mathbb Z_p$. A technique for generating transitive functions via conjugating the function $f(x)=x+1$ by the bijective differentiable modulo $p^n$ functions is described.

Keywords: differentiable modulo $p^n$ functions, transitive functions, bijective functions, conjugation.

UDC: 512.552.18

DOI: 10.17223/2226308X/8/10