Banakh, Taras and Gavrylkiv, Volodymyr:
*Difference bases in finite Abelian groups.*
Acta scientiarum mathematicarum, (85) 1-2.
pp. 119-137. (2019)

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## Abstract

A subset B of a group G is called a difference basis of G if each element g ∈ G can be written as the difference g = ab−1 of some elements a, b ∈ B. The smallest cardinality |B| of a difference basis B ⊂ G is called the difference size of G and is denoted by ∆[G]. The fraction ð[G] := ∆[G]/ p |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 ≥ 11, any finite Abelian p-group G has difference characteristic ð[G] < p−1 √p−3 · supk∈N ð[Cpk ] < 2 · √p−1 √p−3 . Also we calculate the difference sizes of all Abelian groups of cardinality less than 96.

Item Type: | Article |
---|---|

Journal or Publication Title: | Acta scientiarum mathematicarum |

Date: | 2019 |

Volume: | 85 |

Number: | 1-2 |

Page Range: | pp. 119-137 |

ISSN: | 2064-8316 |

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

Uncontrolled Keywords: | Matematika |

Additional Information: | Bibliogr.: p. 136-137. ; összefoglalás angol nyelven |

Official URL: | http://www.acta.hu |

Date Deposited: | 2019. Sep. 25. 10:06 |

Last Modified: | 2019. Sep. 25. 10:06 |

URI: | http://acta.bibl.u-szeged.hu/id/eprint/62136 |

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