Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Isomorphisms of adjoint Chevalley groups over integral domains
HTML articles powered by AMS MathViewer

by Yu Chen PDF
Trans. Amer. Math. Soc. 348 (1996), 521-541 Request permission


It is shown that every automorphism of an adjoint Chevalley group over an integral domain containing the rational number field is uniquely expressible as the product of a ring automorphism, a graph automorphism and an inner automorphism while every isomorphism between simple adjoint Chevalley groups can be expressed uniquely as the product of a ring isomorphism, a graph isomorphism and an inner automorphism. The isomorphisms between the elementary subgroups are also found having analogous expressions.
  • Paul C. Eklof and Alan H. Mekler, Almost free modules, North-Holland Mathematical Library, vol. 46, North-Holland Publishing Co., Amsterdam, 1990. Set-theoretic methods. MR 1055083
  • Armand Borel and Jacques Tits, Homomorphismes “abstraits” de groupes algébriques simples, Ann. of Math. (2) 97 (1973), 499–571 (French). MR 316587, DOI 10.2307/1970833
  • N. Bourbaki, Éléments de mathématique. Fasc. XXXVII. Groupes et algèbres de Lie. Chapitre II: Algèbres de Lie libres. Chapitre III: Groupes de Lie, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1349, Hermann, Paris, 1972. MR 0573068
  • R. W. Carter and Y. Chen, Automorphisms of affine Kac-Moody groups and related Chevalley groups over rings, J. Algebra 155 (1993), no. 1, 44–94. MR 1206622, DOI 10.1006/jabr.1993.1031
  • Y. Chen, Isomorphic Chevalley groups over integral domains, Rend. Sem. Mat. Univ. Padova 92 (1994), 231–237.
  • H. S. Vandiver, Certain congruences involving the Bernoulli numbers, Duke Math. J. 5 (1939), 548–551. MR 21, DOI 10.1215/S0012-7094-39-00546-6
  • M. Demazure, A. Grothendieck, Sch$\acute e$mas en groupes III, Springer–Verlag, New York, 1970.
  • J. E. Humphreys, On the automorphisms of infinite Chevalley groups, Canadian J. Math. 21 (1969), 908–911. MR 248143, DOI 10.4153/CJM-1969-099-7
  • Robert Steinberg, Automorphisms of finite linear groups, Canadian J. Math. 12 (1960), 606–615. MR 121427, DOI 10.4153/CJM-1960-054-6
  • R. Steinberg, Lectures on Chevalley groups, 1967.
  • Giovanni Taddei, Normalité des groupes élémentaires dans les groupes de Chevalley sur un anneau, Applications of algebraic $K$-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983) Contemp. Math., vol. 55, Amer. Math. Soc., Providence, RI, 1986, pp. 693–710 (French). MR 862660, DOI 10.1090/conm/055.2/1862660
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 20G35, 20E36
  • Retrieve articles in all journals with MSC (1991): 20G35, 20E36
Additional Information
  • Yu Chen
  • Affiliation: Department of Mathematics, University of Turin, Via Carlo Alberto 10, 10123 Torino, Italy
  • Email:
  • Received by editor(s): May 2, 1994
  • Additional Notes: Supported in part by Italian M.U.R.S.T. research grant
  • © Copyright 1996 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 348 (1996), 521-541
  • MSC (1991): Primary 20G35, 20E36
  • DOI:
  • MathSciNet review: 1329529