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Weyl ǵroups and finite Chevalley ǵroups

Published online by Cambridge University Press:  24 October 2008

R. W. Carter
R. W. Carter
Affiliation:
University of Warwick
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Extract

In his fundamental paper (1) Chevalley showed how to associate with each complex simple Lie algebra L and each field K a group G = L(K) which is (in all but four exceptional cases) simple. If K is a finite field GF(q), G is a finite group of order

where l is the rank of L, m is the number of positive roots of L and d is a certain integer determined by L and K. The integers m1, m2,…,m1 are determined by L only and satisfy the condition

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 67 , Issue 2 , March 1970 , pp. 269 - 276
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Chevalley, C.Sur certains groupes simplex. Tóhoku Math. J. 7 (1955), 14–66.Google Scholar
(2)Curtis, C. W.The Steinberg character of a finite group with a (B, N)-pair. J. Algebra 4 (1966), 433–441.CrossRefGoogle Scholar
(3)Iwahori, N.On the structure of a Hecke ring of a Chevalley group over a finite field. J. Fac. Sci. Univ. Tokyo, Sect. 1, 10 (1964), 215–236.Google Scholar
(4)Jacobson, N.Lie algebras (Interscience, New York).Google Scholar
(5)Solomon, L.The orders of the finite Chevalley groups. J. Algebra 3 (1966), 376–393.CrossRefGoogle Scholar
(6)Steinberg, R.Variations on a theme of Chevalley. Pacific J. Math. 9 (1959), 875–891.CrossRefGoogle Scholar
(7)Steinberg, R.Endomorphisms of linear algebraic groups. Mem. Amer. Math. Soc. 80 (1968).Google Scholar