Difference bases in dihedral groups
عنوان مقاله: Difference bases in dihedral groups
شناسه ملی مقاله: JR_THEGR-8-1_005
منتشر شده در در سال 1398
شناسه ملی مقاله: JR_THEGR-8-1_005
منتشر شده در در سال 1398
مشخصات نویسندگان مقاله:
Taras Banakh - Ivan Franko National University of Lviv (Ukraine), and Institute of Mathematics, Jan Kochanowski University in Kielce (Poland)
Volodymyr Gavrylkiv - Vasyl Stefanyk Precarpathian National University, Ivano-Frankivsk, Ukraine
خلاصه مقاله:
Taras Banakh - Ivan Franko National University of Lviv (Ukraine), and Institute of Mathematics, Jan Kochanowski University in Kielce (Poland)
Volodymyr Gavrylkiv - Vasyl Stefanyk Precarpathian National University, Ivano-Frankivsk, Ukraine
A subset $B$ of a group $G$ is called a {\em difference basis} of $G$ if each element $g\in G$ can be written as the difference $g=ab^{-۱}$ of some elements $a,b\in B$. The smallest cardinality $|B|$ of a difference basis $B\subset G$ 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 $n\in N$ the dihedral group $D_{۲n}$ of order $۲n$ has the difference characteristic $\sqrt{۲}\le\eth[D_{۲n}]\leq\frac{۴۸}{\sqrt{۵۸۶}}\approx۱.۹۸۳$. Moreover, if $n\ge ۲\cdot ۱۰^{۱۵}$, then $\eth[D_{۲n}]<\frac{۴}{\sqrt{۶}}\approx۱.۶۳۳$. Also we calculate the difference sizes and characteristics of all dihedral groups of cardinality $\le۸۰$.
کلمات کلیدی: dihedral group, difference basis, difference characteristic
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1194961/