Coset-wise affine functions and cycle types of complete mappings

被引：5

作者：

Bors, Alexander ^{[1
]}

Wang, Qiang ^{[1
]}

机构：

[1] Carleton Univ, Sch Math & Stat, 1125 Colonel Dr, Ottawa, ON K1S 5B6, Canada

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2022年 / 83卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Finitefield; Completemapping; Cycletype; Cyclestructure; Wreathproduct; COMPLETE PERMUTATION POLYNOMIALS; FINITE-FIELDS; NUMBER;

D O I：

10.1016/j.ffa.2022.102088

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let K be a finite field of characteristic p. We study a certain class of functions K-+ K that agree with an Fp-affine function K-+ K on each coset of a given additive subgroup W of K - we call them W-coset-wise Fp-affine functions of K. We show that these functions form a permutation group on K with the structure of an imprimitive wreath product and characterize which of them are complete mappings of K. As a consequence, we are able to provide various new examples of cycle types of complete mappings of K - for instance, if p > 2, then all cycle types where each cycle has length a power of p are achieved by complete mappings of K. (c) 2022 Elsevier Inc. All rights reserved.

引用

页数：32

共 37 条

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Bateman P.T., 1950, Am. Math. Mon., V57, P623

[2] HARMONIOUS GROUPS [J].