Treffer: A new upper bound for the cross number of finite abelian groups: A new upper bound for the cross number of finite Abelian groups.
Title:
A new upper bound for the cross number of finite abelian groups: A new upper bound for the cross number of finite Abelian groups.
Authors:
Contributors:
Centre de Mathématiques Laurent Schwartz (CMLS), École polytechnique (X), Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris)-Centre National de la Recherche Scientifique (CNRS)
Source:
Israel Journal of Mathematics. 172:253-278
Publication Status:
Preprint
Publisher Information:
Springer Science and Business Media LLC, 2009.
Publication Year:
2009
Subject Terms:
Finite abelian groups, Inverse problems of additive number theory, including sumsets, cross number, Group Theory (math.GR), 0102 computer and information sciences, 11R27, 11B75, 11P99, 20D60, 20K01, 05E99, 13F05, 01 natural sciences, [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], 20D60, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], FOS: Mathematics, Mathematics - Combinatorics, Number Theory (math.NT), 0101 mathematics, Arithmetic and combinatorial problems involving abstract finite groups, 11P99, 11B75, 20K01, Mathematics - Number Theory, Davenport constant, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], zero-sum sequences, 11R27, Other combinatorial number theory, little cross numbers, zero-sumfree sequences, 13F05, Combinatorics (math.CO), finite Abelian groups, 05E99, Mathematics - Group Theory
Document Type:
Fachzeitschrift
Article<br />Other literature type
File Description:
application/xml
Language:
English
ISSN:
1565-8511
0021-2172
0021-2172
DOI:
10.1007/s11856-009-0072-3
DOI:
10.48550/arxiv.0712.0331
Access URL:
http://arxiv.org/pdf/0712.0331
http://arxiv.org/abs/0712.0331
https://arxiv.org/pdf/0712.0331v1
https://arxiv.org/abs/0712.0331
https://ui.adsabs.harvard.edu/abs/2007arXiv0712.0331G/abstract
https://www.arxiv-vanity.com/papers/0712.0331/
https://link.springer.com/article/10.1007%2Fs11856-009-0072-3
https://link.springer.com/content/pdf/10.1007%2Fs11856-009-0072-3.pdf
https://arxiv.org/pdf/0712.0331
https://hal.archives-ouvertes.fr/docs/00/17/96/77/PDF/PreprintCrossNumber.pdf
https://hal.archives-ouvertes.fr/hal-00179677
http://arxiv.org/abs/0712.0331
https://arxiv.org/pdf/0712.0331v1
https://arxiv.org/abs/0712.0331
https://ui.adsabs.harvard.edu/abs/2007arXiv0712.0331G/abstract
https://www.arxiv-vanity.com/papers/0712.0331/
https://link.springer.com/article/10.1007%2Fs11856-009-0072-3
https://link.springer.com/content/pdf/10.1007%2Fs11856-009-0072-3.pdf
https://arxiv.org/pdf/0712.0331
https://hal.archives-ouvertes.fr/docs/00/17/96/77/PDF/PreprintCrossNumber.pdf
https://hal.archives-ouvertes.fr/hal-00179677
Rights:
Springer TDM
arXiv Non-Exclusive Distribution
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....c5fe660b579f028669fe9b2a6be18d0c
Database:
OpenAIRE
Weitere Informationen
In this paper, building among others on earlier works by U. Krause and C. Zahlten (dealing with the case of cyclic groups), we obtain a new upper bound for the little cross number valid in the general case of arbitrary finite Abelian groups. Given a finite Abelian group, this upper bound appears to depend only on the rank and on the number of distinct prime divisors of the exponent. The main theorem of this paper allows us, among other consequences, to prove that a classical conjecture concerning the cross and little cross numbers of finite Abelian groups holds asymptotically in at least two different directions.
21 pages, to appear in Israel Journal of Mathematics