Irreducible Linear Groups of Degree Four over a Quaternion Division Algebra that Contain a Root Subgroup

REFERENCES

• Bashkirov , E. L. ( 1992 ). Linear groups that contain the commutant of an orthogonal group of index greater then 1 . Siberian Math. J. 33 ( 5 ): 754 – 759 . [CSA]
   Web of Science ®Google Scholar
• Bashkirov , E. L. ( 1993a ). Linear groups generated by two long subgroups . Siberian Math. J. 34 ( 2 ): 210 – 217 . [CSA] [CROSSREF]
   Google Scholar
• Bashkirov , E. L. ( 1993b ). Linear groups contained between two special linear groups over various skew fields . Vestsı¯ Akad Navuk Belarusi. Ser. Fı¯z. Mat. Navuk ( 3 ): 106 – 108 ( in Russian ). [CSA]
   Google Scholar
• Bashkirov , E. L. ( 1994 ). On subgroups of the special linear group of degree 2 over the field of generalized quaternions . Vestsı¯ Akad Navuk Belarusı¯. Ser. Fı¯z. Mat. Navuk ( 1 ): 34 – 39 . ( in Russian ). [CSA]
   Google Scholar
• Bashkirov , E. L. ( 1996a ). On subgroups of the special linear group of degree 2 over an infinite field . Sbornik: Mathematics 187 ( 2 ): 175 – 192 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Bashkirov , E. L. (1996b). Linear groups that contain a root subgroup. Siberian Math. J. 37(6):1086–1100. [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Bashkirov , E. L. ( 1998 ). On subgroups of the general linear group over a skew field of quaternions that contain the special unitary group . Sibirsk. Mat. Zh. 39 ( 6 ): 1251 – 1266 ( in Russian ). [CSA]
   Google Scholar
• Bashkirov , E. L. ( 2001 ). On subgroups of the general linear group of degree four over a quaternion division ring that contain the special unitary group of index 2 . Manuscript deposited in VINITI, no. 1914–V2001. 20 pages (in Russian ). [CSA]
   Google Scholar
• Bashkirov , E. L. ( 2002a ). On subgroups of the general linear group of degree four over a quaternion division algebra that contain the special unitary group of index 1 . St. Petersburg Math. J. 13 ( 3 ): 363 – 372 . [CSA]
   Google Scholar
• Bashkirov , E. L. ( 2002b ). The group Spin 8 and some subgroups of the unitary group of degree four over a quaternion division algebra . St. Petersburg Math. J. 13 ( 3 ): 373 – 388 . [CSA]
   Google Scholar
• Bashkirov , E. L. ( 2002c ). Linear groups over a skew field of quaternions containing the group T n (A, Φ) over a subsfield . Arch. Math. ( Basel ) 79 : 321 – 327 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Bashkirov , E. L. ( 2003a ). On subgroups of the general linear group over the skew field of quaternions which included the symplectic group . Sibirsk. Mat. Zh. 44 ( 2 ): 279 – 290 ( in Russian ). [CSA]
   Google Scholar
• Bashkirov , E. L. ( 2003b ). Some completely reducible linear groups over a quaternion division ring, containing a root subgroup . Comm. Algebra 31 ( 12 ): 5727 – 5754 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Bashkirov , E. L. ( 2004 ). Irreducible linear groups of degree 3 over a quaternion division ring, containing a root subgroup . Comm. Algebra 32 ( 5 ): 1747 – 1763 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Bashkirov , E. L. ( 2005 ). Irreducible linear groups of degree four over a quaternion division ring that contain a subgroup diag(T 3 (K, Φ0), 1) . J. Algebra 287 : 319 – 350 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Cuypers , H. ( 1994 ). Symplectic geometries, transvection groups, and modules . J. Comb. Theory, Ser. A 65 : 39 – 59 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Cuypers , H. , Steinbach , A. ( 1999 ). Linear transvection groups and embedded polar spaces . Invent. Math. 137 : 169 – 198 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Dieudonné , J. ( 1997 ). Géométrie des Groups Classiques . Berlin : Springer-Verlag .
   Google Scholar
• Li , S. ( 1989 ). Irreducible subgroups of GL(n, K) generated by root subgroups . Geom. Dedicata 31 : 41 – 44 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Steinbach , A. I. ( 1997 ). Subgroups of classical groups generated by transvections or Siegel transvections I, II . Geom. Dedicata 68 : 281 – 322 , 323 – 257 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Timmesfeld , F. G. ( 1990 ). Groups generated by k-transvections . Invent. Math. 100 : 167 – 206 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Timmesfeld , F. G. ( 1991 ). Groups generated by k-root subgroups . Invent. Math. 106 : 575 – 666 . [CSA] [CROSSREF]
   Google Scholar
• Timmesfeld , F. G. ( 1994 ). Subgroups generated by root elements of groups generated by k-root subgroups . Geom. Dedicata. 49 : 293 – 321 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Timmesfeld , F. G. ( 1999 ). Abstract root groups and quadratic action . Adv. Math. 142 : 1 – 150 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Vavilov , N. A. ( 1989 ). Linear groups generated by one parameter groups of one dimensional transformations . Russ. Math. Surv. 44 : 265 – 266 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Communicated by M. Dixon.
   Google Scholar