| 主要研究成果: 1. 证明了有限李型单群由它的子群格唯一确定。 2. 确定了任意体上各类典型群中含根子群的全部极大子群。 3. 确定了任意体上各类典型群中若干重要类型子群的全部扩群, "若干重要类型"包括: 子空间稳定子群, 直和分解的稳定子群, 扩体上空间结构的稳定子群, 张量积结构的稳定子群, 一类典型群中所包含的另一类典型群, 等. 4. 将Aschbacher1984年关于有限典型群极大子群的可能类型的定理向任意域上作了一定程度的推广, 确定了任意域中正规化可约子群或可解子群的极大子群的可能类型. 主要论著: 专著: 典型群的子群结构,上海科学技术出版社《现代数学丛书》,1998. 论文目录: 1.李尚志,查建国, 典型群的极大子群的一些结果,中国科学技术大学学报, 第11卷第2期(1981),124-125. 2.李尚志, 关于若干有限单群的子群体系,中国科学技术大学博士论文汇编第一辑(七八级研究生). 3.李尚志,查建国, 有限域上射影特殊酉群的几类极大子群,中国科学(A辑), 1982,2: 125-131. 4.Li Shangzhi & Zha Jianguo, On certain classes of maximal subgroups in projective special unitary groups over finite fields, Scientia Sinica (Ser.A), Vol.25 (1982) No.8, 808-815. (MR 84b: 20056). 5.曾肯成,李尚志,查建国, 关于有限李型单群子群体系的若干结果,全国第一届代数学学术会议大会报告 , (南京, 1982年4月). 6.李尚志,查建国, 射影辛群 PSp(n,F) 中几类极大子群,中国科学(A辑),1982,6:481-486. 7.Li Shangzhi & Zha Jianguo, On certain classes of maximal subgroups in PSp(2n,F), Scientia Sinica (Ser.A),Vol.25 (1982) No.12, 1250-1257. (MR 84h: 20033). 8.李尚志,有限典型群中含根子群的极大子群, 科学通报, 第28卷第5期(1983),257-260.(MR 86a:20054). 9.Li Shangzhi, On the maximality of certain orthogonal groups embedded in symplectic and unitary groups resp., 数学研究... 主要研究成果: 1. 证明了有限李型单群由它的子群格唯一确定。 2. 确定了任意体上各类典型群中含根子群的全部极大子群。 3. 确定了任意体上各类典型群中若干重要类型子群的全部扩群, "若干重要类型"包括: 子空间稳定子群, 直和分解的稳定子群, 扩体上空间结构的稳定子群, 张量积结构的稳定子群, 一类典型群中所包含的另一类典型群, 等. 4. 将Aschbacher1984年关于有限典型群极大子群的可能类型的定理向任意域上作了一定程度的推广, 确定了任意域中正规化可约子群或可解子群的极大子群的可能类型. 主要论著: 专著: 典型群的子群结构,上海科学技术出版社《现代数学丛书》,1998. 论文目录: 1.李尚志,查建国, 典型群的极大子群的一些结果,中国科学技术大学学报, 第11卷第2期(1981),124-125. 2.李尚志, 关于若干有限单群的子群体系,中国科学技术大学博士论文汇编第一辑(七八级研究生). 3.李尚志,查建国, 有限域上射影特殊酉群的几类极大子群,中国科学(A辑), 1982,2: 125-131. 4.Li Shangzhi & Zha Jianguo, On certain classes of maximal subgroups in projective special unitary groups over finite fields, Scientia Sinica (Ser.A), Vol.25 (1982) No.8, 808-815. (MR 84b: 20056). 5.曾肯成,李尚志,查建国, 关于有限李型单群子群体系的若干结果,全国第一届代数学学术会议大会报告 , (南京, 1982年4月). 6.李尚志,查建国, 射影辛群 PSp(n,F) 中几类极大子群,中国科学(A辑),1982,6:481-486. 7.Li Shangzhi & Zha Jianguo, On certain classes of maximal subgroups in PSp(2n,F), Scientia Sinica (Ser.A),Vol.25 (1982) No.12, 1250-1257. (MR 84h: 20033). 8.李尚志,有限典型群中含根子群的极大子群, 科学通报, 第28卷第5期(1983),257-260.(MR 86a:20054). 9.Li Shangzhi, On the maximality of certain orthogonal groups embedded in symplectic and unitary groups resp., 数学研究与评论, 第3卷第1期(1983),101-103. (MR 85c: 20039). 10.Li Shangzhi, On the subgroup lattice characterization of finite simple groups of Lie type, Chinese Annals of Math. (Ser. B) (数学年刊(英文版) ), Vol.4 (1983) No.2, 165-169. (MR 85j: 20019). 11.李尚志, PSL(n,F) 中几类极大子群, 数学学报 ,第26卷第5期(1983),613-621. (MR 85e: 20031). 12.Li Shangzhi, Maximal subgroups containing root subgroups in finite classical groups, Kexue Tongbao , Vol.29 (1984) No.1, 14-18. (MR 86a: 20054). 13.Li Shangzhi & Zha Jianguo, Certain classes of maximal subgroups in classical groups, Lecture at the International Group Theory Symposium (Beijing, Aug.27-Sept.8, 1984) 14.李尚志, POmega(n,F,Q) 中含根子群的极大子群,中国科学(A辑),1985,5:193-205. 15.Li Shangzhi, Maximal subgroups in POmega(n,F,Q) with root subgroups, Scientia Sinica (Ser. A), Vol.28 (1985) No.8, 826-838.(MR 87e: 20079). 16.李尚志,查建国, Sp(2n,F2) 中含长根子群的极大子群, 数学研究与评论, 第5卷第2期(1985),45-48. (MR 87i: 20087). 17.李尚志, PSU(n,K,f)(n(f)>=1) 中含根子群的极大子群, 数学学报, 第29卷第5期(1986), 632-641. (MR 88a: 20062). 18.Shangzhi Li, Maximal subgroups in classical groups, Lecture at the 1986 AMS Summer Institute on "Representations of finite groups and related topics" (Arcata, July 7-25, 1986). 19.Li Shangzhi, Maximal subgroups containing short-root subgroups in PSp(2n,F), Acta Math. Sinica (New Ser.) ( 数学学报 英文版 ), Vol.3 (1987) No.1, 82-91. 20.Shangzhi Li, Maximal subgroups in classical groups over arbitrary fields, Proc. of Symposia in Pure Math., Vol.47 (1987) Part II, 487-493. 21.Li Shangzhi, Maximal subgroups in classical groups over division rings, Lecture at the Sino-US Seminar on classical groups and related areas, (Beijing, May 18-23,1987). 22.李尚志, 体上酉群在线性群中的极大性, 科学通报, 第39卷第21期(1988), 1608-1610. 23.Shangzhi Li, Overgroups of certain subgroups in the classical groups over division rings, Contemp. Math., Vol.82 (1989), 53-57. (MR 90c: 20053). 24.Shangzhi Li, Overgroups in GL(nr,F) of certain subgroups of SL(n,K),I, Journal of Algebra , Vol.125 (1989) No.1, 215-235. (MR 91d: 20051). 25.Shangzhi Li, Irreducible subgroups of SL(n,K) generated by root subgroups, Geom. Dedicata, Vol.31 (1989), 41-44. (MR 90h: 20068). 26.Shangzhi Li, The maximality of monomial subgroups of linear groups over division rings, J.Algebra , Vol.127 (1989), No.1, 22-39. (MR 91b: 20061) 27.Shangzhi Li, Overgroups of SU(n,K,f) or Omega(n,K,Q) in GL(n,K), Geom. Dedicata, Vol.33 (1990), 241-250. (MR 91g: 11038). 28.李尚志, SL(n,K) 在 GL(n,F)(K subset F) 中的扩群, 数学学报, 第33卷第6期(1990), 774-778. (MR 91k: 20049). 29.Shangzhi Li, Overgroups in GL(U otimes W) of certain subgroups of GL(U) otimes GL(W), I, J. Algrbra, Vol.137(1991), No.2, 338-368. (MR 92d: 20039). 30.Shangzhi Li, A new type of classical groups over division rings of characteristic 2, J. Algebra , Vol.138 (1991), No.2, 399-419. (MR 92e: 20033). 31.Shangzhi Li, Overgroups of a unitary group in GL(2,K), J. Algebra, Vol.149 (1992), No.2, 275-286. 32.李尚志, TU(n,K,h) 或 Omega(n,K,Q) 在 GL(nr,F) 中的扩群, 科学通报, 第38卷第17期(1993), 1537-1539. 33.Li Shang-Zhi, Overgroups in GL(nr,F) of TU(n,K,h) or Omega(n,K,Q), Chinese Science Bulletin , Vol.39 (1994), No.1,182-185. 34.Shangzhi Li, Overgroups in GL(n,F) of a Classical Group over a Subfield of F, Algebra Colloq., 1:4(1994), 335-346. 35.Shangzhi Li, On the Subgroup Structure of Classical Groups,Group Theory in China, Science Press, New York Beijing, Kluwer Academic Publishers, Dordrecht Boston London, (1996), 70-90. 36.Shangzhi Li, Maximal Subgroups in the Classical Groups Normalizing Reducible Subgroups, Proceedings of the 1996 Beijing International Conference on Group Theory, Springer-Verlag Singapore Pte.Ltd.1998, p98-105. 37.王登银, 李尚志, L1(F)在L(F)中的扩群,中国科学技术大学学报,第28卷第3期(1998), 284-289. 38.Dengyin Wang (王登银), Shangzhi Li(李尚志), Overgroups of L(K) in L(F), Algebra Colloquium 5:4 (1998) 417-424. 39.Li Libin(李立斌)、Li Shangzhi(李尚志),Quantum Comodule Approach the Solution of the Quantum Yang-Baxter Equation, 数学物理学报 2000,20B(2):206-212。 40.Li Libin(李立斌)、Li Shangzhi(李尚志),Quantum Yang-Baxter modules and a generalized Notion of the Drinfeld Quantum Double, Proc.of the International Conference on Representation Theory ,China Higher Education Press & Springer-Verlag. 41.王登银, 李尚志, Kantor定理成立的必要条件及其应用, 数学年刊, 22A:3 (2001), 319-322. 42.Q.W.Wang, S.Z. Li, On the center (Skew)- Self-conjugate solutions to the systems of matrix equations over a finite dimensional central algebra, Mathematical Sciences Research Hot-Line , 2001年第12期(11-17). 43.李尚志,陈发来,《数学实验》课程建设的认识与实践,数学的实践与认识第31卷第6期. 44.李尚志,卫宗礼,欧氏环上辛群在线性群中的扩群,中国科学技术大学学报,第32卷第2 期(2002年4月)127-134. 45.李尚志,李治,卫宗礼,主理想整环上线性群中直和因子定驻子群的扩群,中国科学技术大学学报,第32卷第3期(2002年6月)259-265. 46.Q.W. Wang, S.Z. Li, The linear matrix equations over a division ring, Math.Sci.Res. J., 6(5)(2002): 249-253. 47.Q.W.Wang , Ai-Yun Wang,S.Li, Bi(skew) symmetric and bipositive semidefinite solutions to a system of linear matrix equations over division rings, Math.Sci.Res.J.,6(7)(2002),333-339. 48.Li Li-bin, Li Shangzhi, Quantum Groups by Ore extensions associated with group algebras, J. Of Math Research & Exposition,22(2)(May 2002) 205-211. 49.Q.W.Wang,J.H.Sun & S.Z Li, Consistency fo bi(skew)symmetric solutions to systems of generalized Sylvester equations over a finite central algebra, Linear Algebra Appl. 353(2002):169-182. 50.SUN Jianhua, LI Shangzhi, Some Constructions of Twisted Hopf Algebras, Math.Sci.Res.J. 6(7)(2002),354-360. 51.孙建华,李尚志,分次环与模范畴上的伴随函子, 数学杂志 ,vol.22(2002)No.3,349-353. 52.Qingwen Wang, Shangzhi LI, A practical method for finding the central solution to a system of linear matrix equations over an arbitrary division ring, Math.Sci.Res.J.6(11)(2002), 542-547. 53.Shangzhi Li, Subgroup structure of classical groups, International algebraic Conf. (St.Petersburg, Russia, Sept 17-23,2002) 54.Qingwen Wang, Shangzhi Li, Systems of matrix equations over a central algebra, J. Math. Research & Exposistion, Vol.23,No.1,15-20,Feb,2003, 15-20. 55.Wang Qingwen, Sun Jianhua, Li Shangzhi, On the Centro-symmetric and Centro-skew-symmetric Solutions to a Matrix Equation over a Central Algebra, Chin.Quart.J.of Math., 2003,18(2):111-116.
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