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Bibliography
E. Artin, Geometric Algebra, Wiley Interscience, New York, 1957.
A. Bak, On modules with quadratic forms, pp. 55–66, in Lecture Notes in Mathematics 108, Springer Verlag, Berlin 1969.
A. Bak, K-Theory of Forms, Annals of Mathematics Studies 98, Princeton University Press, 1981.
A. Bak, Le probleme des sous-groupes de congruence et le probleme metaplectique pour les groupes classiques de rang >1, C.R. Acad. Sc. Paris, 292, 307–310 (1981).
A. Bak and U. Rehann, The congruence subgroup and metaplectic problems for SLN>2 of division algebras, J. Algebra, 78 (1982), 475–547.
H. Bass, Algebraic K-Theory, Benjamin, New York, 1968.
H. Bass, Unitary Algebraic K-Theory, pp. 57–265, in Lecture Notes in Mathematics 343, Springer Verlag, Berlin 1973.
H. Bass, Introduction to some Methods of Algebraic K-Theory, American Mathematical Soc., Providence, R.I., 1974.
H. Bass, Clifford algebras and spinor norms over a commutative ring, Amer. J. Math. 96 (1974), 156–206.
H. Bass, J. Milnor, and J.P. Serre, Solution of the Congruence Subgroup Problem for SLn and Sp2n. Publ. Math. IHES 33 (1967), 59–137.
D. Callan, The isomorphisms of unitary groups over non-commutative domains, J. Algebra 52 (1978), 475–503.
F. Connolly, Linking numbers and surgery, Topology 12, 1973, 389–409.
V.V. Deodhar, On central extensions of rational points of algebraic groups, Amer. J. Math. 100 (1978), 303–386.
J. Dieudonne, La Geometrie des Groupes Classiques, 3rd ed., Springer Verlag, Berlin-New York, 1971.
P. Draxl, Skew Fields, Cambridge University Press, 1982.
A. Fröhlich and E.M. McEvett, Forms over rings with involution, J. Algebra, 12 (1969), 79–104.
I. Golubchik, On the general linear group over an associative ring, Uspekhi Mat. Nauk, 28:3 (1973), 179–180 (Russian).
A. Hahn, Isomorphism theory for orthogonal groups over arbitrary integral domains, J. Algebra, 51 (1978), 233–287.
A. Hahn, Category equivalences and linear groups over rings, J. Algebra, 77 (1982), 505–543.
A. Hahn, A hermitian Morita theorem for algebras with anti-structure, J. Algebra, 93 (1985), 215–235.
A. Hahn and Z.X. Li, Hermitian Morita theory and hyperbolic unitary groups, to appear in J. Algebra.
A. Hahn, D. James and B. Weisfeiler, Homomorphisms of algebraic and classical groups: a survey, in Canadian Mathematical Society Conference Proceedings, Volume 4 (1984), 249–296.
I. Hambleton, L. Taylor and B. Williams, An introduction to maps between surgery obstruction groups, pp. 49–127, in Lecture Notes in Mathematics 1051, Springer Verlag 1982.
J. Humphreys, Arithmetic Groups, Lecture Notes in Mathematics 789, Springer Verlag, Berlin, 1980.
D. James, W. Waterhouse and B. Weisfeiler, Abstract homomorphisms of algebraic groups: problems and bibliography, Comm. Algebra, 9 (1981), 95–114.
W. van der Kallen, Generators and relations in Algebraic K-Theory, pp. 305–210, in Proceedings of the International Conference of Mathematicians, Helsinki, 1978.
W. van der Kallen, Stability for K2 in Dedekind rings of arithmetic type, pp. 217–248, in Lecture Notes in Mathematics 854, Springer-Verlag, Berlin, 1980.
M. Kolster, Surjective stability for unitary K-groups, preprint, 1975.
M. Kolster, General symbols and presentation of elementary linear groups, J. für reine u. angew. Math. 353 (1984), 132–164.
T.Y. Lam, The Algebraic Theory of Quadratic Forms, 2nd ed., Benjamin, New York, 1980.
K. Leung, The isomorphism theory of projective pseudo-orthogonal groups, J. Algebra, 61 (1979), 367–387.
J. Mennicke, Zur Theorie der Siegelschen Modulgruppe, Math. Ann. 159 (1965), 115–129.
H. Matsumoto, Sur les sousgroupes arithmetiques des groupes semisimple deployes, Ann. Sci. Ecole Norm. Sup. (4) 2(1969), 1–62.
A. Merkurjev and A. Suslin, K-Cohomologies of Severi-Brauer varieties and norm residue homomorphism, Izv. Akad. Nauk SSSR, 16 (1982), 1011–1046.
J. Milnor, Introduction to algebraic K-Theory, Annals of Mathematical Studies 72, Princeton University Press, 1971.
N.M. Mustafa-Zade, On epimorphic stability of a unitary K2-functor, Russian Math. Surveys (1980), 99–100.
O.T. O'Meara, Lectures on Linear groups, Amer. Math. Society, Providence, R.I., 1974.
O.T. O'Meara, A general isomorphism theory for linear groups, J. Algebra, 44 (1977), 93–142.
O.T. O'Meara, Symplectic groups, Math. Surveys, Amer. Math. Soc. Providence, R.I., 1978.
O.T. O'Meara, A survey of the isomorphism theory of the classical groups, pp. 225–242, in "Ring theory and Algebra III", Dekker, New York, 1980.
W. Pender, Automorphisms and Isomorphisms of the indefinite modular classical groups, Ph.D. Thesis, Sydney University (1972).
W. Pender, Classical groups over division rings of characteristic 2, Bull. Aust. Math. Soc. 7 (1972), 191–226.
G. Prasad and M.S. Ragunathan, On the congruence subgroup problem: determination of the "metaplectic kernel", Invent. math. 71, (1983), 21–42.
H.G. Quebbemann, W. Scharlau, and M. Schulte, Quaratic and hermitian forms in additive and abelian categories, J. Algebra, 59 (1979), 264–289.
A. Ranicki, The algebraic theory of surgery I, Foundations, Proc. London Math. Soc. (3) 40 (1980), 87–192.
A. Ranicki, Exact Sequences in the Algebraic Theory of Surgery, Princeton Mathematical Notes, Princeton University Press, 1981.
H.S. Ren and Z.X. Wan, Automorphisms of PSL+2 (K) over any skew field K, Acta. Math. Sinica, 25, (1982), 484–492.
J.P. Serre, Trees, Springer-Verlag, Berlin, New York, 1980.
R. Sharpe, On the structure of the unitary Steinberg group, Ann. Math. 96 (1972), 444–479.
J. Silvester, Introduction to Algebraic K-Theory, Chapman and Hall, London, 1981.
G. Soule, K2 et le groupe de Brauer [d'apres A.S. Merkurjev et A.A. Suslin]. Seminare Bourbaki, 1982/83, No. 601 (1982).
R. Steinberg, Generateurs, relations et revetements de groups algebriques, Colloque de Bruxelles, 1962, 113–127.
R. Steinberg, Lecture Notes on Chevalley Groups, Yale University, 1967.
A. Suslin, On the structure of the special linear group over polynomial rings, Math. USSR Izvestija, Vol. II (1972), No. 2, 221–328.
A. Suslin and V. Kopeiko, Quadratic modules and the orthogonal group over polynomial rings, Zap. Naucn. Sem. Leningrad. Otdel. Math. Inst. Steklov. (LOMI) 71 (1977), 216–250.
A. Suslin, Reciprocity laws and the stable rank of polynomial rings, Math. USSR Izvestija, Vol 15(1980), No. 3, 589–623.
R. Swan, K-Theory of Finite Groups and Orders, Lecture Notes in Mathematics 149, Springer-Verlag, Berlin, 1970.
J. Tits, Buildings of spherical type and finite BN-pairs, Lecture Notes in Mathematics 383, Springer-Verlag, Berlin, 1974.
L. Vaserstein, Stabilization of unitary and orthogonal groups over a ring with involution, Math. USSR Sbornik, Vol. 10 (1970), 307–326.
L. Vaserstein, The stabilization for classical groups over rings, Math. USSR Sbornik 22, (1974), 271–303.
L. Vaserstein, Foundations of algebraic K-theory, Russian Math. Surveys, 31:4 (1976), 89–156.
L. Vaserstein, On the normal subgroups of GLn over a ring, pp. 456–465, in Lecture Notes in Mathematics 854, Springer-Verlag, Berlin, 1981.
L. Vaserstein, On full subgroups in the sense of O'Meara, J. Algebra, 75 (1982), 437–44.
L. Vaserstein, Classical groups over rings, in Canadian Mathematical Society Conference Proceedings, Volume 4 (1984).
L. Vaserstein and A. Suslin, Serre's problem on projective modules over polynomial rings and algebraic K-theory, Math. USSR Izvestija, Vol. 10 (1976), No. 5, 937–1001.
A. Wadsworth, Merkurjev's elementary proof of Merkurjev's theorem, Boulder Conference in Algebraic K-theory, to appear.
C.T.C. Wall, Surgery on Compact Manifolds, Academic Press, 1970.
C.T.C. Wall, On the axiomatic foundation of the theory of Hermitian forms, Proc. Camb. Phil. Soc., 67 (1970), 243–250.
C.T.C. Wall, Foundations of algebraic L-Theory, pp. 266–300, in Lecture Notes in Mathematics 343, Springer Verlag, Berlin, 1973.
C.T.C. Wall, On the classification of Hermitian Forms III, semisiple rings, Invent. Math., 18 (1972), 119–141.
G.E. Wall, The Structure of a unitary factor group, Publ. Math., IHES, No. 1, (1959), 7–23.
Z.X. Wan, The Classical Groups, Shanghai University Press, 1981.
Z.X. Wan and J.G. Yang, Automorphisms of the projective quaternion unimodular group in dimension 2, Chinese Annals of Math., 3(1982), 395–402.
B. Weisfeiler, Abstract homomorphisms of big subgroups of algebraic groups, pp. 135–181, in Topics in the theory of Algebraic Groups, Notre Dame Mathematical Lectures, No. 10, University of Notre Dame Press, 1982.
J.S. Wilson, The normal and subnormal structure of general linear groups, Proc. Camb. Phil. Soc. 71(1972), 163–177.
Zalesky, Linear groups, Russian Math. Surveys, 36, No. 5, (1981), 63–128.
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Hahn, A.J. (1986). Algebraic K-theory, morita theory, and the classical groups. In: Tuan, HF. (eds) Group Theory, Beijing 1984. Lecture Notes in Mathematics, vol 1185. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076172
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