My research interest is in the areas of groups, rings, group rings and combinatorial number theory.  The group ring of a group G over a commutative ring K is the ring KG of all formal finite sums α = ∑ a_gg and is an attractive object of study.  Here, group theory, ring theory, commutative algebra and number theory come together in a fruitful way, and moreover the study of group rings has important applications in coding theory.  My recent research work has thrown light on the structures of group rings and their unit groups.

The zero-sum theory is an emerging branch in additive and combinatorial number theory. The two starting points are the Erdös-Ginzburg- Ziv theorem (1961) and the introduction of the Davenport constant (1963). The former states that for the cyclic group C_n, every sequence of 2n-1 elements contains a zero-sum subsequence of n elements. The latter is related to non-unique factorization in algebraic number theory, and in 1963, H. Davenport introduced an invariant D(G) (so called the Davenport constant of a finite group G), which is the least positive integer t such that every sequence of t elements has a non-empty zero-sum subsequence.

In this new branch, zero-sum (or zero-sum free) sequences and related invariants such as the Davenport constant, the EGZ constant, the Gao constant and their relationships are investigated. A typical direct zero-sum problem is to find the exact values (or estimate a best upper (or lower) bound of a given invariant), while an indirect zero-sum problem is to characterize the structures of those zero-sum (or zero-sum free) sequences on which the best bound of a specific invariant achieves.

A few years ago, I started a new exciting research initiative and extended my research interest into this new branch by investigating a few zero-sum problems and the related invariants such as the Davenport constant, EGZ-constant and the Gao Constant. I have already made several significant contributions in this area (see the list of my publications for details).

• Jian Cui, Yuanlin Li*, Josh MacIntyre+, and Daniel Teeuwsen+ Nil clean group rings over metacyclic groups , Journal of Algebra and Its Application, to appear (2026) 2650167 (14 pages)
• Weidong Gao*, Wanzhen Hui+, Xiao Jiang, Yuanlin Li and Xiaoyan Wang On zero-sum subsequences of cross number 1 , Acta Arith. 219 (2025), no 4, 347-363.
• Yongke Qu*, YUanlin Li, Qinghong Wang and Xiaoyue Zhao, A note on additive bases of abelian groups of rank 2 , Graphs Combin. 41 (2025), no. 1, Paper No. 24 (https://doi.org/10.1007/S00373-025-02895-9).
• Yongke Qu, Yuanlin Li* and Daniel Teeuwsen+, On the small Davenport constant for finite groups , Isral J. Math. 267(2025). 397-419 ( https://www.doi.org/10.1007/s11856-024-2707-9)
• Zhengxing Li* and Yuanlin Li, Class-preserving Coleman automorphisms of Frobenius groups, Publ.Math. Debrecen, 105(2024), 59-66.
• Adam Alhassan, Yilan Tan+* and Yuanlin Li, ON B(5; 20) 2-GROUPS, Algebra Colloq. 31(2024), no 3, 429-440.
• Weidong Gao, Wanzhen Hui+*, Xue Li, Yuanlin Li, Yongke Qu and Qinghai Zhong, ON GENERALIZED NARKIEWICZ CONSTANTS OF FINITE ABELIAN GROUPS, Acta Arith. 212 (2024), no. 2, 133–172.
• Wanzhen Hui+, Meiling Huang and Yuanlin Li* Inverse zero-sum problem of finite abelian groups of rank 2, Colloq. Math. 175(2024), no 1, 77-95.
• Haobai Wang+ and Yuanlin Li*, Perfect matching and zero-sum 3-magic labeling, J. Combin. Math. and Combin. Comput. 117 (2023), 209–216.
• Peng*, M. Wang, Y. Hui and Y. Li, Inverse problems associated subsequence sums in C_p⊕ C_pI I , Discrete Math. 346 (2023), no. 8, Paper No. 113422, 10 pp.
• Wanzhen Hui+, Yuanlin Li*, Jiantao Peng and Mingrui Wang Inverse problems associated with k-sums of sequences over finite abelian groups, Acta Math. Hungar. 169 (2023), no. 1, 312–324.
• Yongke Qu and Yuanlin Li*, On a conjecture of Zhuang and Gao, Colloq. Math. 171 (2023), no. 1, 113-126.
• Siao Hong*+, Meiling Huang and Yuanlin Li, A sharp upper bound for the sum of reciprocals of least common multiplies II, Bull. Aust. Math. Soc. 107 (2023), no.1, 10-21.
• Yongke Qu and Yuanlin Li*, Extremal product-one free sequences and |G|-product-one free sequences of a metacyclic group, Discrete Mathematics, 345 (2022), No. 8, Paper No. 112938, 17pp.
• Weidong Gao, Yuanlin Li, Yongke Qu* and Qinghong Wang, Additive bases of finite abelian groups of rank 2, Integers, 22 (2022), Paper No. A37, 15 pp.
• Yongke Qu, Yuanlin Li* and Daniel Teeuwsen+, On a conjecture of the small Davenport constant for finite groups, Journal of Combinatorial Theory, 189 (2022), Paper No. 105617, 14 pp.
• Yuanlin Li and Qinghai Zhong*, On clean, weakly clean, and feebly clean commutative group rings, Journal of Algebra and Its Applications, No. 5 (2022), Paper No. 2250085 33 pp, (https://doi.org/10.1142/S0219498822500852).
• Yongke Qu and Yuanlin Li*, Additive bases of C₃ ⊕ C_3q, Colloq. Math.169 (2022) no. 2, 189 – 195.r
• Weidong Gao, Yuanlin Li* and Yongke Qu, On the invariant E(G) for groups of odd order, Acta Arith. 201 (2021), no. 3, 255-267.
• Yunpeng Bai, Yuanlin Li and Jiangtao Peng*, Unit groups of finite group algebras of Abelian groups of order 17 to 20, AIMS Mathematics, 6 (2021), no. 6, 7305-7317.
• Jian Cui, Yuanlin Li* and Haobai Wang+ On Nil Clean Group Rings, Comm. Algebra, 49 (2021), no.2, 790-796.
• Peng*, Y. Li, C. Liu+ and M. Huang, On the inverse problems associated with subsequence sums of zero-sum free sequences over finite abelian groups, Colloq. Math. 163 (2021), no. 2, 317-332.
• Jiangtao Peng+, Yongke Qu and Yuanlin Li*, On the inverse problems associated with subsequence sums in C_p ⊕ C_p, Front. Math. China, 15 (2020), no. 5, 985–1000.
• Peng+, Y. Li*, C. Liu+ and M. Huang, On subsequence sums of a zero-sum free sequence over finite abelian groups, J. Number Theory, 217 (2020), 193-217.
• Zeng and Y. Li*, The structure of minimal zero-sum sequences of length five, Ars Combinatoria, 151 (2020), 41-61.
• Li and Q. Zhong*, Clean group rings over localizations of rings of integers, J. Pure and Applied Algebra, 224 (2020), no. 7, 106284 (https://doi.org/10.1016/j.jpaa.2019.106284).
• Gao*, M. Huang, W. Hui+, Yuanlin Li, C. Liu+ and J. Peng, Sums of sets of abelian group elements, J. Number Theory, 208 (2020), 208-229.
• Sun, J. Peng* and Y. Li, A note on the inverse problems associated with subsequence sums, JCMCC (Journal of Combinatorial Mathematics and Combinatorial Computing), 111 (2019) 3-8.
• Peng, W. Hui+, Y. Li* and F. Sun, On subset sums of zero-sum free sets of abelian groups, Int. J. Number Theory, 15 (3), (2019) 645-654.
• Gao*, Y. Li, C. Liu+ and Y. Qiu, product one subsequences over subgroups of a finite group, Acta Arith. 189 (2019), no. 3, 209–221.
• Gao, Y. Li, J. Peng and G. Wang*, A unifying look at zero-sum invariants, Int. J. Number Theory, 14(3) (2018) 705-711.
• Xia, Y. Li* and J. Peng, Minimal zero-sum sequences of length five over finite cyclic groups of prime power order, Ars Combinatoria, 135 (2017) 369-390.
• Zeng*, P. Yuan and Y. Li, On the structure of long unsplittable minimal zero-sum sequences, Acta Arith. 176 (2) 2016, 131-159.
• Zhengxing Li*, Yuanlin Li and Hongwei Zhao, The influence of maximal quotient groups on the normalizer conjecture of integral group rings, J. Group Theory, 19 (6)(2016) 983-992.
• Huang+, Y. Li*, and P. Yuan,Star-clean group rings II, Comm. Algebra,44 (7) (2016) 3171-3181.
• Zhengxing Li and Yuanlin Li*, Class-preserving Coleman automorphisms of permutational wreath products with 2-closed base groups, J. Algebra Appl. 15 (10) (2016) 1650189 (11 pages).
• Gao*, Yuanlin Li, P. Zhao+ and J. Zhuang, On sequences over a finite abelian group with zero-sum subsequences of forbidden lengths, Colloq. Math. 144 (1) (2016) 31- 44 (DOI:10.4064/ cm6488-8-2015).
• Yuan and Y. Li* Long unsplittable zero-sum sequences over a finite cyclic group, Int. J. Number Theory, 12, (4)(2016)979-993( DOI: 10.1142/S1793042116500615).
• Huang+ and Y. Li* On B(5,18) groups, Comm. Algebra, 44 (2) (2016) 568-690 (DOI: 10.1080/00927872.2014.981751).
• Zhengxing Li* and Yuanlin Li, Coleman automorphisms of generalized dihedral groups, Acta Mathematica Sinica (English Series) 32 (2) (2016) 251-257.
• Huang+, Y. Li* and G. Tang On *-clean non-commutative group rings, J. Algebra Appl. 15 (8) (2016) 1650150 (17 pages).
• Aliniaeifard*+, M. Behboodib and Y. Li, The Annihilating-Ideal Graph of a Ring, J. Korean Math. Soc. 52 (6) (2015) 1323-1336.
• Gao, Y. Li*, P. Yuan and J. Zhuang, On the structure of long zero-sum free sequences and n-zero-sum free sequences over finite cyclic groups, Arch. Math.(Basel), 105 (4) (2015) 361-370 (DOI: 10.1007/s00013-015-0813-y ).
• X, Zeng, Yuanlin Li* and P. Yuan, On a conjecture of Lemke and Kleitman, Acta Arith. 168 (3) (2015) 289-299.
• Hongdi Huang+ and Yuanlin Li*, On B(4,14) non-2-groups, J. Algebra Appl. 14, (7) (2015) 1550118 (14 pages).
• Yanyan Gao*+, Jianlong Cheng and Yuanlin Li, Some ∗-clean group rings, Algebra Colloq. 22 (1) (2015) 169-180.
• Yuanlin Li*, M. M. Parmenter and Pingzhi Yuan On Star-clean group rings, J. Algebra Appl. 14 (1) (2015) 1550004 (11pages).
• Tongsuo Wu*, Dancheng Lu and Yuanlin Li, On zero divisors and prime elements of bounded semirings, Front. Math. China, 9 (6) (2014) 1381-1399.
• Xia*, C. Shen and Yuanlin Li, On the index of length four minimal zero-sum sequences, Colloq. Math. 135 (2) (2014), 201-209.
• Gao*, Yuanlin Li and J. Peng, An Upper Bound for the Davenport Constant of Finite Groups, Journal of Pure and Applied Algebra, 218 (10) (2014), 1838-1844.
• Aliniaeifard+ and Yuanlin Li*, Zero-divisor Graphs for Group Rings, Comm. Algebra, 42 (11) (2014), 4790-4800.
• Gaohua Tang, Yangjiang Wei and Yuanlin Li*, Unit groups of group algebras of some small groups, Czechoslovak Math. Journal. 64 (139) (2014), 149-157.
• Yuanlin Li* and M.M. Parmenter, Central units in integral group rings II, International journal of Algebra, 8 (2014) 47-55.
• Yuanlin Li* and Yilan Tan+, On B-5 Groups, Ars Combin, 114, (2014) 3-14.
• Jiangtao Peng+ and Yuanlin Li*, Minimal zero-sum sequences of length five over finite cyclic groups, Ars. Combin. 112 (2013) 373-384.
• Aliniaeifard+, Yuanlin Li* and K. Nicholson, Morphic p-groups, Journal of Pure and Applied Algebra, 217 (2013) 1864-1869.
• Yuanlin Li* and Jiangtao Peng+, Minimal zero-sum sequences of length four over finite cyclic groups II, Int. J Number Theory, 9 (2013) 845-866.
• Yuanlin Li*, and Xiaoying Pan, On B(5,k) groups, Bull. Aust. Math. Soc. 84 (2011) 393-407.
• Weidong Gao*, Yuanlin Li and Jiangtao Peng, A quantitative aspect of non-unique factorizations: the Narkiewicz constants II, Colloq. Math. 124 (2011) 205-218.
• Yuanlin Li* and Yilan Tan+, On B(4,13) 2-Groups, Comm. Algebra, 39 (10) (2011) 3769-3780.
• Weidong Gao and Yuanlin Li*, Remarks on group rings and Davenport’s constant, Ars Combinatoria, CI (2011), 417-423.
• Weidong Gao*, Yuanlin Li, Jiangtao Peng, Chris Plyley+ and Guoqing Wang, On the index of sequences over cyclic groups, Acta Arith. 148, No. 2, 119-134 (2011).
• Gao and Yuanlin Li* On Duo group rings, Algebra Colloq. 18 (1) (2011) 163-170.
• Bell and Yuanlin Li*, On a combinatorial commutativity condition for rings, Comm. Algebra, 39 (1) (2011) 601-607.
• Yuanlin Li*, C. Plyley+, P. Yuan and X. Zeng, Minimal Zero Sum Sequences of Length Four over Finite Cyclic Groups, Journal of Number Theory, 130 (2010) 2033-2048.
• Yuanlin Li and K. Nicholson*, Ehrlich’s Theorem for Groups, Bull. Austral. Math. Soc. 81 (2010) 304-309.
• Yuanlin Li and K. Nicholson* and L. Zan, Morphic groups, Journal of Pure and Applied Algebra, 214 (2010) 1827-1834.
• Yuanlin Li* and Yilan Tan+, On B(4,k) groups, Journal of Algebra and Its Applications, 9 (2010) 27-42.
• Gao* and Yuanlin Li The Erdös-Ginzburg-Ziv theorem for finite solvable groups, J. Pure Appl. Algebra, 214 (2010) 898-909.
• Ding*, Yuanlinm Li and L. Mao J-coherent rings, Journal of Algebra and Its Applications, 8(2009) 139-155.
• Ding*, Yuanlin Li and L. Mao, Strongly Gorenstein Flat Modules, J. Austral. Math. Soc., 86(2009) 323-338.
• Li and M.M. Parmenter* Graded reversibility in integral group rings, Acta Applicandae Mathematicae, 108 (2009) 129-133.
• Gao*, Y. Li, J. Peng and F. Sun On subsequence sums of a zero-sum free sequence II, E. J. Combinatorics, 15 (1) 2008 R117.
• Gao*, Y. Li, J. Peng and F. Sun Subsums of a zero-sum free subset of an abelian group, E. J. Combinatorics, 15 (1) 2008 R116.
• Zsolt Balogh and Yuanlin Li*, On the derived length of the group of units of a group algebra, Journal of Algebra and Its Applications, 6 (6) (2007) 991-999.
• Yuanlin Li* and M.M. Parmenter, Reversible group rings over commutative rings, Comm. Algebra, 35 (12) (2007) 4096-4104.
• Yuanlin Li*, Strongly clean matrix rings over local rings, Journal of Algebra, 312 (2007), 397-404.
• H.E. Bell and Yuanlin Li*, Duo group rings, Journal of Pure and Applied Algebra, 209(3)(2007), 833-838.
• Herman and Yuanlin Li*, Trivial torsion units in G-adapted group rings, Journal of Algebra and Its Applications, 5(6) (2006), 781-791.
• Yuanlin Li*, H.E. Bell and C. Phipps, On reversible group rings, Bulletin of The Australian Mathematical Society, 74 (2006), 139-142.
• Herman and Yuanlin Li*, Class preserving automorphisms of Blackburn groups, Journal of The Australian Mathematical Society, 80 (2006), 351-358.
• Jianlong Chen, Yuanlin Li* and Yiqiang Zhou Morphic group rings, Journal of Pure and Applied Algebra, 205 (2006) 621-639.
• Herman and Yuanlin Li* Trivial units for group rings over rings of algebraic integers, Proceedings of American Mathematical Society, 134, (2006), 631-635.
• E.G. Goodaire*, Yuanlin Li and M.M. Parmenter Hypercentral units in alternative loop rings, Journal of Algebra, 283 (2005), 317-326.
• Yuanlin Li* and M.M. Parmenter Upper central series of the unit group of an integral group ring, Communications in Algebra, 33 (2005), 1409-1415.
• Herman, Yuanlin Li* and M.M. Parmenter Trivial units for Group rings with G-adapted coefficient rings, Canadian Mathematical Bulletin, 48 (2005), 80-89.
• Yuanlin Li* and M.M. Parmenter Some results on hypercentral units in integral group rings, Communications in Algebra, 31 (2003),no 7,3207-3217.
• Yuanlin Li On the normalizer problem for G-adapted group rings of torsion groups, Bulletin of the Australian Mathematical Society, 67 (2003), no 1, 171-176.
• Yuanlin Li On the normalizer problem of integral group rings of torsion groups, Israel Journal of Mathematics, 132 (2002), 169-176.
• Yuanlin Li The normalizer of a metabelian group in its integral group ring, Journal of Algebra, 256 (2002), no 2, 343-351.
• Jianlong Chen, Nanqing Ding*, Yuanlin Li and Yiqiang Zhou On (m. n)-injectivity of modules, Communications in Algebra, 29 (2001), no 12, 5589-5603.
• Edgar Goodaire and Yuanlin Li* The normalizer conjecture in the alternative case, Algebra Colloquium, 8 (2001) 455-462.
• Yuanlin Li Some results on bicyclic units in an integral group ring, Communications in Algebra, 29 (2001) no 3, 1339-1345.
• M.M. Parmenter and Yuanlin Li*, Hypercentral Units in Integral Group Rings, Proc. Amer. Math. Soc., 129 (2001) no 8, 2235-2238.

Modern Algebra (Groups, Rings, Modules, and Group Rings) (5P10)

Topics in Groups (5P11)

Ring Theory (5V76) and Algebraic Coding Theory (5V77) (for graduate students)

Advanced Group Theory (4P11)

Advanced Ring Theory (4P13)

Advanced Mathematical Structures: Group Algebra (4P14)

Abstract and Applied Algebra (3P13 and 3P12)

(Abstract) Linear Algebra (2P12 and 2P13)

Postdoctoral researchers

Dr. Wanzhen Hui (2023)
Dr. Siao Hong (2022)
Dr. Cao Liu (2018 – 2019)
Dr. Jiangtao Peng (2009)

VIS

Dr. Yushuang Fan (2025 – 2026)
Dr. Weidong Gao (2025)
Dr. Yongke Qu (2020 – 2021)
Dr. Jian Cui (2020)
Dr. Jiwen Zeng (2019)
Dr. Wujie Shi (2019)
Dr. Jiangtao Peng (2018 – 2019)
Dr. Lijuan Qian (2016 – 2019)
Dr. Xiangneng Zeng (2016)
Dr. Zhengxing Li (2015)
Dr. Greg Lee (2015)
Dr. Yushuang Fan (2014)
Dr. Jujuan Zhuang (2014 – 2015)
Dr. Pingzhi Yuan (2014)
Dr. Keith Nicolson (2011)
Dr. Tongsuo Wu (2010)
Dr. Hourong Qin (2008)
Dr. Xizhong Zheng  (2007)
Dr. Lixing Mao (2007)
Dr. Z. Balogh (2006 – 2007)
Dr. Nanqing Ding (2006)
Dr. Jianlong Chen (2004)
Dr. Yue Liu (2004)

PhD students co-supervised

Co-supervised with Dr. Weidong Gao at Nankai University, China

• Wanzhen Hui (2019, Completed June 2022)
• Xue Li (2019, Completed July 2021)
• Siao Hong (2017, Completed July 2021)
• Chao Liu (2017, Completed July 2018)
• Hanbing Zhang (2014, Completed Aug 2017)
• Pingping Zhao (2014, Completed Aug 2016)

Co-supervised with Dr. J. Chen at Southeast University, China

• Honglin Zhou (2014 – 2018)
• Yanyan Gao (2012, Completed Sep. 2013) 

MSc students

Joshua Mac Intyre (2023 – 2025)
Daniel Teeuwsen (2020 – 2022)
Haobai Wang (2019 – 2021)
Jiachao Wu (co-supervised with Prof. Fukś) (2018 – 2020)
Yuchen Jin (co-supervised with Prof. Fukś) (2018 – 2020)
Maryam Molakarimi (2016 – 2018)
Vannesa Hamilton (2014 – 2016)
Hongdi Huang (2013 – 2015)
Farid Aliniaeifard (2011 – 2013)
Vivian Apety (2011 – 2013)
Xiaoying Pan (2009 – 2011)
Chris Plyley (2007 – 2009)
Yilan Tan (2007 – 2009)

Undergraduate research students (MATH 4F90)

Brayden Ricard (2025)
Emma Roden (2023)
Tyler Nelson (2014 – 2015)
Vanessa Hamilton (2013 – 2014)
Jesse Ireland (2011 – 2012)
Jesse Larone (2011 – 2012)
Tyson Moss (2011)
Bryan Penfound (2007)
Jason Lizotte (2007)
Colin Phipps (2005 – 2006)
Kaisheng Tang (2004 – 2005)
Amy Mcneely (2003 – 2004)
Congfeng Lin (2003)