35
Views
8
CrossRef citations to date
0
Altmetric
Original Articles

Some Completely Reducible Linear Groups over a Quaternion Division Ring Containing a Root Subgroup

Pages 5727-5754 | Received 01 Mar 2002, Published online: 01 Feb 2007

References

  • Bashkirov , E. L. 1993 . Linear groups contained between two special linear groups over various skew fields. (Russian) . Vests Akad. navuk Belarus Ser. Fz. Mat. Navuk , : 106 – 108 .
  • Bashkirov , E. L. 1994 . Subgroups of the special linear group of degree 2 over the skew field of generalized quaternions. (Russian) . Vests Akad. navuk Belarus Ser. Fz. Mat. Navuk , : 34 – 39 .
  • Bashkirov , E. L. 1996a . On subgroups of the special linear group of degree 2 over an infinite field . Sbornik: Mathematics , 187 : 175 – 192 .
  • Bashkirov , E. L. 1996b . Linear groups that contain a root subgroup . Siberian Math. J. , 37 : 1086 – 1100 .
  • Bashkirov , E. L. 1998 . On subgroups of the general linear group over the skew field of quaternions containing the special unitary group. (Russian) . Sibirsk. Math. Zh. , 39 : 1251 – 1266 .
  • Bashkirov , E. L. 2001a . The subgroups of the general linear group of degree four over a quaternion division algebra, that contain the special unitary group of index 1. (Russian) . Algebra i Analiz , 13 ( 3 ) : 18 – 42 . English translation in: St. Petersburg Math. J. 2002, 13:353–372
  • Bashkirov , E. L. 2001b . The group Spin8 and some subgroups of the unitary group of degree four over a quaternion division algebra. (Russian) . Algebra i Analiz , 13 ( 3 ) : 43 – 64 . English translation in: St. Petersburg Math. J. 2002, 13:373–388
  • Bashkirov , E. L. 2003 . On subgroups of the general linear group over a quaternion division ring that contain the symplectic group . Siberian Math. J. , 44
  • Bashkirov, E. L. Irreducible linear groups of degree 3 over a quaternion division ring containing a root subgroup. Comm. Algebra (to appear)
  • Cameron , P. J. and Hall , J. I. 1991 . Some groups generated by transvection subgroups . J. Algebra , 40 : 184 – 209 .
  • Cuypers , H. 1994 . Symplectic geometries, transvection groups, and modules . J. Comb. Theory Ser. A , 65 : 39 – 59 .
  • Cuypers , H. and Steinbach , A. 1999 . Linear transvection groups and imbedded polar spaces . Invent. Math. , 137 : 169 – 198 .
  • Dieudonné , J. 1952 . On the structure of unitary groups . Trans. Amer. Math. Soc. , 72 : 367 – 385 .
  • Dieudonné , J. 1997 . La Géométrie des Groupes Classiques Berlin : Springer Verlag .
  • Jacobson , N. 1996 . Finite Dimensional Division Algebras Over Fields 278 Berlin : Springer Verlag .
  • Li Shangzhi . 1989 . Irreducible subgroups of SL(n, K) generated by root subgroups . Geom. Dedicata , 31 : 41 – 44 .
  • Merzlyakov , Yu. I. 1973 . Linear groups . J. Soviet math. , 1 : 571 – 593 .
  • Steinbach , A. 1997 . Subgroups of classical groups generated by transvections or siegel transformations. I, II . Geom. Dedicata , 68 : 281 – 322 . 323–357
  • Timmesfeld , F. G. 1990 . Groups generated by k-transvections . Invent. Math. , 100 : 167 – 206 .
  • Timmesfeld , F. G. 1999 . Abstract root subgroups and quadratic action . Adv. Math. , 142 : 1 – 150 .
  • Vavilov , N. A. 1989 . Linear groups generated by one parameter groups of one dimensional transformations . Russ. Math. Surv. , 44 : 265 – 266 .
  • Vavilov , N. A. 1995 . “ Intermediate subgroups in Chevalley groups ” . In Groups of Lie Type and Their Geometries , Math. Soc. Note Ser. No. 207 Edited by: Kantor , W. M. and Martino , L. D. 233 – 280 . London : Cambridge University Press .
  • Wehrfritz , B. A. F. 1973 . Infinite Linear Groups 229 New York : Springer Verlag .
  • Zalesskii , A. E. 1981 . Linear groups . Russ. Math. Surv. , 36 : 56 – 107 .
  • Zalesskii , A. E. 1985 . Linear groups . J. Sov. Math. , 31 : 2974 – 3004 .
  • Zalesskii , A. E. 1989 . Linear groups . Itogi Nauki i Techniki, Fundamental Trends of Math. , 37 : 114 – 228 .
  • Zalesskii , A. E. and Serežkin , V. N. 1976 . Linear groups generated by transvections. (Russian) . Izv. Akad. Nauk SSSR Ser. Mat. , 40 : 26 – 49 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.