研究领域

有限群论、有限群表示论，特别是融合系及相关局部结构范畴理论。

论文与著作

1.     Jie Jian, Jun Liao* & Heguo Liu，Criteria for nilpotency of fusion systems，Journal of Algebra and Its Applications，(2026) 2650161

2.     刘合国, 张继平, 赵静*, 徐行忠, 廖军, 关于Seksenbaev-Robinson定理, 数学年刊A辑, 2024, 45(2): 185-204

3.     Jie Jian, Jun Liao* & Heguo Liu, The kernels of powers of linear operator via Weyr characteristic, Linear and Multilinear Algebra, 73:2, 193-208

4.     刘合国, 张继平, 徐行忠*, 廖军, 多重循环群的一个注记, 数学学报（中文版）, 2023, 66(3): 399-404

5.     J.Liao, H. Liu, X.Luo, and X. Xu, On the Residual Finiteness of a Class of Infinite Soluble Groups, Algebra Colloquium 30: 1 (2023) 155—164

6.     刘合国, 高睿*, 徐行忠, 廖军, 一类无限Cernikov p群的自同构群, 数学年刊A辑, 2022, 43(1): 73--94

7.     R. Gao*, J.Liao, H. Liu and X. Xu, On the Unitriangular Groups over Rational Numbers Field, Acta Mathematica Sinica, English Series, Apr., 2022, Vol. 38, No. 4, pp. 718–734

8.     R. Gao, J.Liao, H. Liu*, H.Xiong, and X. Xu, A Note on Systems of Equations of Power Sums, Mathematical Notes, 2022, 111 (6): 855–869

9.     雒晓良, 刘合国, 徐行忠, 廖军*. 一类多重循环群的剩余有限性质, 数学年刊A辑(中文版). 2021, 42(01): 33–46

10.  J. Liao, H. Liu, X. Xu, J. Zhang, Finitely generated nilpotent groups of infinite cyclic commutator subgroups, Acta. Math. Sin. English Ser., 36(2020), no. 12: 1315–1340

11.  J. Liao, H. Liu, J. Zhang, Fusions systems over Mp(1, 1, 1) × A-groups, Acta. Math. Sin. English Ser. 35 (2019), no. 8, 1311—1320

12.  Ellen Henke and Jun Liao, Control of fusion by Abelian subgroups of the hyperfocal subgroup, J. Algebra Appl. 17, 1850024 (2018) [11 pages] 

13.  刘合国, 张继平, 廖军. 换位子群是不可分Abel群的有限秩可除幂零群. 数学年刊A辑(中文版), 2018, 39(03):287-296. Translation in Chinese J. Contemp. Math. 39 (2018), no. 3, 253--262.

14.  J. Liao, H. Liu, J. Zhang, Fusion systems over non-resistant A2-groups, Journal of Algebra, 485(2017), 199-212.

15.  Jun Liao, Heguo Liu, Zuohui Wu & Huan Xiong, Kernels for certain kinds of linear transformations, Linear and Multilinear Algebra, 65 (2017): 6, 1131-1141.

16.  刘合国, 吴佐慧, 张继平, 徐行忠, 廖军. Frattini子群是无限循环群的有限生成幂零群. 数学学报中文版, 60 (2017), no.3, 465—474.

17.  J. Liao, Y. Liu, Minimal non-nilpotent and locally nilpotent fusion systems, Algebra Colloq., 23(2016), no. 3, 455—462.

18.  J. Liao, J. Zhang, Saturated fusion systems over A2-groups. Math. Z., 282 (2016), no. 3, 1137—1147.

19.  J. Liao, On exotic saturated fusion systems, Acta Mathematica Sinica, English Series, 32 (2016), no. 4, 457—462.

20.  J. Liao, J. Zhang, Nilpotent fusion systems. J. Algebra, 442 (2015), 438—454.

21.  J. Liao, H. Liu, M. Shao, X. Xu, A matrix identity and its applications. Linear Algebra Appl. 471(2015), 346—352.

22.  J. Liao, H. Liu, Y. Wang, Z. Wu, and X. Xu. Generalization of Gracia’s Results. Electronic Journal of Linear Algebra, 30 (2015), 243—252.

23. 刘合国, 吴佐慧, 张继平, 徐行忠, 廖军. 无限循环群被有限生成Abel群的中心扩张. 数学年刊, 36 (2015), no. 3, 233—246; translation in Chinese J. Contemp. Math. 36 (2015), no. 3, 207—218.

荣誉与奖励

1. 参与建设国家级线下一流本科课程，排名第三：高等代数，国家级线下一流本科课程，主持人：徐运阁，团队成员：陈媛、廖军、李丽莎、张坤，获批时间2023.05。

2. 参与编写课程教材，排名第三：徐运阁、章超、廖军，高等代数，科学出版社，2021年7月。