The DOI matches its Crossref record; 149 of the 152 references it cites were found in a registry or an index.
Zero-sum problems in finite abelian groups: A survey
Open accessOverview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“Theorem 1.1 If G is a finite abelian group of order n , then E ( G ) = D ( G )+ n -1 .”
From Davenport constant with weights (2010) · cites this paper as [7]
Citations
Cites
Alon, N. (1999) · Combinatorics Probability Computing · doi:10.1017/s0963548398003411 · Cited by 653
Lang, S. (1991) · Encyclopaedia of mathematical sciences · doi:10.1007/978-3-642-58227-1 · Cited by 513
Additive number theory: inverse problems and the geometry of sumsets
(1997) · Choice Reviews Online · doi:10.5860/choice.35-0343a · Cited by 414
Non-Unique Factorizations: Algebraic, Combinatorial and Analytic Theory
Geroldinger, A., & Halter-Koch, F. (2006) · doi:10.1201/9781420003208 · Cited by 366
Self-citationHooley, C. (1967) · Journal für die reine und angewandte Mathematik (Crelles Journal) · doi:10.1515/crll.1967.225.209 · Cited by 353
Foundations of a Structural Theory of Set Addition
Freiman, G. (2007) · Translations of Mathematical Monographs · doi:10.1090/mmono/037 · Cited by 347
There are Infinitely Many Carmichael Numbers
Alford, W. R., Granville, A., & Pomerance, C. (1994) · The Annals of Mathematics · doi:10.2307/2118576 · Cited by 333
A combinatorial problem on finite Abelian groups, I
Olson, J. E. (1969) · Journal of Number Theory · doi:10.1016/0022-314x(69)90021-3 · Cited by 290
Cyclic Spaces for Grassmann Derivatives and Additive Theory
da Silva, J. A. D., & Hamidoune, Y. O. (1994) · Bulletin of the London Mathematical Society · doi:10.1112/blms/26.2.140 · Cited by 174
Motwani, R., & Raghavan, P. (1995) · Cambridge University Press eBooks · doi:10.1017/cbo9780511814075.015 · Cited by 148
Research works printed but not linked: 20
- Bialostocki, 2000, Zero-sum ascending waves, J. Combin. Math. Combin. Comput., 32, 103
- Bialostocki, 1990, Zero sum Ramsey theorems, Congr. Numer., 70, 119
- A. Bialostocki, M. Lotspeich, Some developments of the Erdős–Ginzburg–Ziv theorem, in: Sets, Graphs and Numbers, vol. 60, Colloquia Mathematica Societatis Janos Bolyai, North-Holland, Amsterdam, New York, 1992, pp. 97–117.
- Chapman, 2002, On Davenport's constant of finite abelian groups, Far East J. Math. Sci., 2, 47
- Chiaselotti, 1993, Sums of distinct elements in finite abelian groups, Boll. Unione Mat. Ital., 7, 243
- Dimitrov, 2004, On the strong Davenport constant of nonabelian finite p-groups, Math. Balkica, 18, 131
- Erdős, 1961, Theorem in the additive number theory, Bull. Res. Council Israel, 10, 41
- M. Freeze, Lengths of factorizations in Dedekind domains, Ph.D. Thesis, University of North Carolina at Chapel Hill, 1999.
- Freeze, 2001, Sumsets of zerofree sequences, Arab J. Sci. Eng. Section C: Theme Issues, 26, 97
- Z. Füredi, D.J. Kleitman, The minimal number of zero sums. in: Combinatorics, Paul Erdős is Eighty, J. Bolyai Mathematical Society, 1993, pp. 159–172.
- Gallardo, 2000, On Brakemeier's variant of the Erdős–Ginzburg–Ziv problem, Tatra Mt. Math. Publ., 20, 91
- W. Gao, Some problems in additive group theory and number theory, Ph.D. Thesis, Sichuan University, Sichuan, PR China, 1994.
- Gao, 1996, An improvement of Erdős–Ginzburg–Ziv theorem, Acta Math. Sin., 39, 514
- Gao, 2000, Zero sums in finite cyclic groups, Integers, 0, 9
- Kemnitz, 1983, On a lattice point problem, Ars. Combin., 16-B, 151
- Krause, 1991, Arithmetic in Krull monoids and the cross number of divisor class groups, Mitt. Math. Ges. Hamb., 12, 681
- E. Lipkin, Subset sums of sets of residues. in: Structure Theory of Set Addition, vol. 258, Astérisque, 1999, pp. 187–192.
- Ordaz, 2006, On zero-free sets, Divulg. Mat., 14, 1
- Schmid, 2005, Half-factorial sets in finite abelian groups: a survey, Grazer Math. Ber., 348, 41
- Skałba, 1992, The relative Davenport's constant of the group Zn×Zn, Grazer Math. Ber., 318, 167
Cited by
Local tameness of v -noetherian monoids
Geroldinger, A., & Hassler, W. (2008) · Journal of Pure and Applied Algebra · doi:10.1016/j.jpaa.2007.10.020 · Cited by 61
Self-citationGao, W., & Geroldinger, A. (2008) · Monatshefte für Mathematik · doi:10.1007/s00605-008-0547-z · Cited by 59
Self-citationThe Interplay of Invariant Theory with Multiplicative Ideal Theory and with Arithmetic Combinatorics
Cziszter, K., Domokos, M., & Geroldinger, A. (2016) · Springer proceedings in mathematics & statistics · doi:10.1007/978-3-319-38855-7_3 · Cited by 50
Self-citationBlanco, V., García-Sánchez, P. A., & Geroldinger, A. (2011) · Illinois Journal of Mathematics · doi:10.1215/ijm/1373636689 · Cited by 48
Self-citationGao, W., Geroldinger, A., & Schmid, W. A. (2007) · Acta Arithmetica · doi:10.4064/aa128-3-5 · Cited by 47
Self-citation
Metadata
- Authors
- Gao, W., & Geroldinger, A.
- Affiliations
- Nankai University (CN)
- University of Graz (AT)
- Corresponding author
- Geroldinger, Alfred
- Venue
- Expositiones Mathematicae
- Publisher
- Elsevier BV
- Published
- 2006-11
- Volume
- 24
- Issue
- 4
- Pages
- 337-369
- ISSN
- 0723-0869 (ISSN-L)
- OpenAlex
- W2121001629
- Cited by
- 262
- References
- 152
- Citations by year
- 2026: 19 · 2025: 13 · 2024: 13 · 2023: 11 · 2022: 15 · 2021: 15 · 2020: 18 · 2019: 14 · 2018: 11 · 2017: 10 · 2016: 3 · 2015: 13 · 2014: 13 · 2013: 13 · 2012: 11
- FWCI
- 17.93
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- www.elsevier.com/tdm/userlicense/1.0/ (tdm)
- www.elsevier.com/open-access/userlicense/1.0/ (vor, 2452 d)
- Locations
- Expositiones Mathematicae (publishedVersion)
- Funders
- National Natural Science Foundation of China
- Austrian Science Fund
- Topics
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Advanced Combinatorial Mathematics
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Limits and Structures in Graph Theory
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Finite Group Theory Research
- Keywords
- zero-sum problems, finite abelian groups, combinatorial number theory, Davenport constant, algebraic invariants
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Zero-sum problems in finite abelian groups: A survey. https://app.cochat.ai/papers/10.1016/j.exmath.2006.07.002
- The paper
- Gao, W., & Geroldinger, A. (2006). Zero-sum problems in finite abelian groups: A survey. Expositiones Mathematicae. https://doi.org/10.1016/j.exmath.2006.07.002
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.