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  • Difference bases in finite Abelian groups
    Banakh, Taras, 1968- ; Gavrylkiv, Volodymyr
    A subset ▫$B$▫ of a group ▫$G$▫ is called a difference basis of ▫$G$▫ if each element ▫$g\in G$▫ can be written as the difference ▫$g =ab^{-1}$▫ of some elements ▫$a,b\in B$▫. The smallest ... cardinality ▫$|B|$▫ of a difference basis ▫$B\subset G$▫ is called the difference size of ▫$G$▫ and is denoted by ▫$\Delta [G]$▫. The fraction ▫$\partial [G]:=\Delta [G]/\sqrt{|G|}$▫ is called the difference characteristic of ▫$G$▫. Using properties of the Galois rings, we prove recursive upper bounds for the difference sizes and characteristics of finite abelian groups. In particular, we prove that for a prime number ▫$p\geq 11$▫, any finite abelian ▫$p$▫-group ▫$G$▫ has difference characteristic ▫$\partial [G]<\frac{\sqrt{p}-1}{\sqrt{p}-3}\cdot \sup \partial [C_{p^k}]<\sqrt{2}\cdot \frac{\sqrt{p}-1}{\sqrt{p}-3}$▫. Also we calculate the difference sizes of all abelian groups of cardinality less than 96.
    Vir: Acta scientiarum mathematicarum. - ISSN 0001-6969 (Vol. 85, no. 1-2, 2019, str. 119-137)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2019
    Jezik - angleški
    COBISS.SI-ID - 63916803

    Povezava(-e):

    https://doi.org/10.14232/actasm-017-586-x
    DOI

vir: Acta scientiarum mathematicarum. - ISSN 0001-6969 (Vol. 85, no. 1-2, 2019, str. 119-137)
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