Difference bases in dihedral groups

IF 0.7 Q2 MATHEMATICS

International Journal of Group Theory Pub Date : 2017-04-08 DOI:10.22108/ijgt.2017.21612

T. Banakh, V. Gavrylkiv

引用次数: 1

Abstract

A subset $B$ of a group $G$ is called a {em‎ ‎difference basis} of $G$ if each element $gin G$ can be written as the‎ ‎difference $g=ab^{-1}$ of some elements $a,bin B$‎. ‎The smallest‎ ‎cardinality $|B|$ of a difference basis $Bsubset G$ is called the {em‎ ‎difference size} of $G$ and is denoted by $Delta[G]$‎. ‎The fraction ‎‎‎$eth[G]:=Delta[G]/{sqrt{|G|}}$ is called the {em difference characteristic} of $G$‎. ‎We prove that for every $nin N$ the dihedral group‎ ‎$D_{2n}$ of order $2n$ has the difference characteristic‎ ‎$sqrt{2}leeth[D_{2n}]leqfrac{48}{sqrt{586}}approx1.983$‎. ‎Moreover‎, ‎if $nge 2cdot 10^{15}$‎, ‎then $eth[D_{2n}]

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二面体基团中的不同碱基

群$G$的子集$B$称为｛em‎ ‎差基}，如果每个元素$gin G$都可以写成‎ ‎一些元素$a，bin B的差值$g=ab^{-1}$$‎. ‎最小的‎ ‎差基$Bsubset G$的基数$|B|$称为｛em‎ ‎差值大小}为$G$，并用$Delta[G]表示$‎. ‎分数‎‎‎$eth[G]：=Delta[G]/｛sqrt｛|G|｝｝$被称为$G的｛em差分特征｝$‎. ‎我们证明了每$nin N$的二面体群‎ ‎$次序为$2n$的D_{2n}$具有差分特性‎ ‎$sqrt{2}leeth[D_{2n}]leqfrac{48}{sqrt{586}}近似1.983$‎. ‎此外‎, ‎如果$nge 2点10^｛15｝$‎, ‎则$eth[D_{2n}]

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来源期刊

International Journal of Group Theory MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

30 weeks

期刊介绍： International Journal of Group Theory (IJGT) is an international mathematical journal founded in 2011. IJGT carries original research articles in the field of group theory, a branch of algebra. IJGT aims to reflect the latest developments in group theory and promote international academic exchanges.

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