Generalized Commutator Formulas

REFERENCES

• Bak , A. ( 1982 ). Subgroups of the general linear group normalized by relative elementary groups , In: Algebraic K-Theory, Part II . Lecture Notes in Mathematics , Vol. 967 . Berlin : Springer-Verlag , pp. 1 – 22 .
   Google Scholar
• Bak , A. ( 1991 ). Nonabelian K-theory: the nilpotent class of K 1 and general stability . K-Theory 4 : 363 – 397 .
   Google Scholar
• Bak , A. , Hazrat , R. , Vavilov , N. A. ( 2009 ). Localization completion strikes again: relative K 1 is nilpotent by abelian . J. Pure Appl. Algebra 213 : 1075 – 1085 .
   Web of Science ®Google Scholar
• Bak , A. , Vavilov , N. A. ( 1995 ). Normality for elementary subgroup functors . Math. Proc. Camb. Philos. Soc. 118 : 35 – 47 .
   Web of Science ®Google Scholar
• Bak , A. , Vavilov , N. A. ( 2000 ). Structure of hyperbolic unitary groups I: elementary subgroups . Algebra Colloquium 7 : 159 – 196 .
   Web of Science ®Google Scholar
• Bass , H. ( 1968 ). Algebraic K-Theory . New York : Benjamin .
   Google Scholar
• Bass , H. ( 1964 ). K-theory and stable algebra . Inst. Hautes Etudes Sci., Publ. Math. 22 : 5 – 60 .
   Google Scholar
• Gerasimov , V. N. ( 1987 ). The group of units of the free product of rings . Mat. Sbornik 134 : 42 – 65 .
   Google Scholar
• Golubchik , I. Z. ( 1995 ). On the general linear group over weakly Noetherian associative rings . Fundam. Appl. Math. 1 : 661 – 668 .
   Google Scholar
• Golubchik , I. Z. , Mikhalev , A. V. ( 1985 ). On the group of elementary matrices over PI-rings . In: Investigations in Algebra . Iad. Tbil. Gos. Univ., Tbilisi , pp. 20 – 24 .
   Google Scholar
• Khlebutin , S. G. ( 1986 ). Some properties of the elementary subgroup . In: Algebra, Logic, and Number Theory . Izd. Mosk. Gos. Univ. , Moscow , pp. 86 – 90 .
   Google Scholar
• Hahn , A. J. , O'Meara , O. T. ( 1989 ). The Classical Groups and K-Theory . Berlin : Springer .
   Google Scholar
• Hazrat , R. ( 2002 ). Dimension theory and nonstable K 1 of quadratic modules . K-Theory 27 : 293 – 328 .
   Google Scholar
• Hazrat , R. , Vavilov , N. A. ( 2003 ). K 1 of Chevalley groups are nilpotent . J. Pure Appl. Algebra 179 : 99 – 116 .
   Web of Science ®Google Scholar
• Hazrat , R. , Vavilov , N. A. ( 2009 ). Bak's work on the K-theory of rings, with an appendix by Max Karoubi . J. K-Theory 4 : 1 – 65 .
   Web of Science ®Google Scholar
• Mason , A. W. ( 1981 ). On subgroup of GL(n, A) which are generated by commutators, II . J. Reine Angew. Math. 322 : 118 – 135 .
   Google Scholar
• Mason , A. W. ( 1981 ). A further note on subgroups of GL(n, A) which are generated by commutators . Arch. Math. 37 : 401 – 405 .
   Google Scholar
• Mason , A. W. , Stothers , W. W. ( 1974 ). On subgroup of GL(n, A) which are gnerated by commutators . Invent. Math. 23 : 327 – 346 .
   Web of Science ®Google Scholar
• Stepanov , A. ( 1997 ). On the normal structure of the general linear group over a ring . Zap. Nauch. Sem. POMI 236 : 162 – 169 .
   Google Scholar
• Stepanov , A. , Vavilov , N. A. (2000). Decomposition of transvections: a theme with variations. K-Theory 19:109–153.
   Google Scholar
• Suslin , A. A. ( 1977 ). On the structure of the special linear group over the ring of polynomials . Izv. Akad. Nauk SSSR, Ser. Mat. 141 : 235 – 253 .
   Google Scholar
• Tulenbaev , M. S. ( 1979 ). The Schur multiplier of the group of elementary matrices of finite order . Zap. Nauch. Sem LOMI 86 : 162 – 169 .
   Google Scholar
• Vaserstein , L. N. ( 1981 ). On the normal subgroups of GL n over a ring . Lecture Notes in Math. 854 : 456 – 465 .
   Google Scholar
• Vavilov , N. A. , Stepanov , A. V. ( 2008 ). Standard commutator formula . Vestnik St. Petersburg University, Mathematics. 41 : 5 – 8 .
   Google Scholar
• Communicated by V. A. Artamonov.
   Google Scholar