Difference bases in dihedral groups
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Isfahan
2019-03-01
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| Series: | International Journal of Group Theory |
| Subjects: | |
| Online Access: | http://ijgt.ui.ac.ir/article_21612_09abda43cc316d9fccf8681b5cc2872d.pdf |
| Summary: | 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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| ISSN: | 2251-7650 2251-7669 |