Difference Sets Disjoint from a Subgroup III: The Skew Relative Cases

被引：0

作者：

Anderson, Gradin ^{[1
]}

Haviland, Andrew ^{[1
]}

Holmes, Mckay ^{[1
]}

Humphries, Stephen P. ^{[1
]}

Magland, Bonnie ^{[1
]}

机构：

[1] Brigham Young Univ, Dept Math, Provo, UT 84602 USA

来源：

GRAPHS AND COMBINATORICS | 2023年 / 39卷 / 04期

关键词：

Difference set; Subgroup; Hadamard difference set; Schur ring; Dicyclic group;

D O I：

10.1007/s00373-023-02662-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study finite groups G having a subgroup H and D subset of G\H such that (i) the multiset {xy(-1) : x, y is an element of D} has every element that is not in H occur the same number of times (such a D is called a relative difference set); (ii) G = D. D(-1). H; (iii) D boolean AND D(-1) = empty set. We show that vertical bar H vertical bar = 2, that H is central and that G is a group with a single involution. We also show that G cannot be abelian. We give infinitely many examples of such groups, including certain dicyclic groups, by using results of Schmidt and Ito.

引用

页数：20

共 33 条

[21] Grassmannian codes from paired difference sets
Fickus, Matthew
Iverson, Joseph W.
Jasper, John
King, Emily J.
DESIGNS CODES AND CRYPTOGRAPHY, 2021, 89 (11) : 2553 - 2576
[22] Constructions of almost difference sets from finite fields
Ding, Cunsheng
Pott, Alexander
Wang, Qi
DESIGNS CODES AND CRYPTOGRAPHY, 2014, 72 (03) : 581 - 592
[23] Merit factors of polynomials derived from difference sets
Guenther, Christian
Schmidt, Kai-Uwe
JOURNAL OF COMBINATORIAL THEORY SERIES A, 2017, 145 : 340 - 363
[24] Constructions of almost difference sets from finite fields
Cunsheng Ding
Alexander Pott
Qi Wang
Designs, Codes and Cryptography, 2014, 72 : 581 - 592
[25] Asynchronous channel hopping systems from difference sets
Xiaotian Chen
Yue Zhou
Designs, Codes and Cryptography, 2017, 83 : 179 - 196
[26] Asynchronous channel hopping systems from difference sets
Chen, Xiaotian
Zhou, Yue
DESIGNS CODES AND CRYPTOGRAPHY, 2017, 83 (01) : 179 - 196
[27] Paley type sets from cyclotomic classes and Arasu–Dillon–Player difference sets
Yu Qing Chen
Tao Feng
Designs, Codes and Cryptography, 2015, 74 : 581 - 600
[28] Almost Difference Sets From Singer Type Golomb Rulers
Daza Urbano, David Fernando
Martos Ojeda, Carlos Andres
Trujillo Solarte, Carlos Alberto
IEEE ACCESS, 2022, 10 : 1132 - 1137
[29] Paley type sets from cyclotomic classes and Arasu-Dillon-Player difference sets
Chen, Yu Qing
Feng, Tao
DESIGNS CODES AND CRYPTOGRAPHY, 2015, 74 (03) : 581 - 600
[30] Difference Sets Disjoint from a Subgroup II: Groups of Order 4p2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4p^2$$\end{document}
Stephen P. Humphries
Nathan L. Nicholson
Graphs and Combinatorics, 2021, 37 (6) : 2333 - 2349

← 1 2 3 4 →