An A2-proof of Structure Theorems for Chevalley Groups of Types

@inproceedings{2005AnAO,
  title={An A2-proof of Structure Theorems for Chevalley Groups of Types},
  author={},
  year={2005}
}
  • Published 2005
In the present paper we prove the main structure theorem for Chevalley groups G = G(Φ, R) of types Φ = E6, E7 over a commutative ring R. More precisely, we describe subgroups in G normalized by the elementary subgroup E(Φ, R). This result is not new, since structure theorems are known for all Chevalley groups [25, 27, 28, 30], [38]–[40], and [58, 61] (see [42, 65, 34, 56] for further references). The gist of the present paper resides not in the results themselves, but rather in the method of… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-10 of 28 references

Arrangement of subgroups in the general linear group over a commutative ring

Z. I. Borevich, N. A. Vavilov
Trudy Mat. Inst. Steklov. 165 (1984), 24–42; English transl. in Proc. Steklov Inst. Math. 1985, no. 3. MR0752930 • 2005
View 15 Excerpts
Highly Influenced

Normalité des groupes élémentaires dans les groupes de Chevalley sur un anneau

G. Taddei
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. MR0862660 • 2005
View 16 Excerpts
Highly Influenced

On the structure of parabolic subgroups

H. Azad, M. Barry, G. M. Seitz
Comm. Algebra 18 (1990), 551–562. MR1047327 • 2004
View 4 Excerpts
Highly Influenced

Chevalley Groups over Commutative Ringsi

View 6 Excerpts
Highly Influenced

Serre’s problem on projective modules over polynomial rings

L. N. Vasershtĕın, A. A. Suslin
and algebraic K-theory, Izv. Akad. Nauk SSSR Ser. Mat. 40 (1976), no. 5, 993–1054; English transl. in Math. USSR-Izv. 10 • 1976
View 6 Excerpts
Highly Influenced

Sur les sous-groupes arithmétiques des groupes semi-simples déployés

H. Matsumoto
Ann. Sci. École Norm. Sup. (4) 2 (1969), 1–62. MR0240214 • 1566
View 4 Excerpts
Highly Influenced

Simple groups of Lie type

R. Carter
Pure Appl. Math., vol. 28, John Wiley, London et al., 1972. MR0407163 • 1094
View 4 Excerpts
Highly Influenced

Normality of the elementary subgroups of twisted Chevalley groups over commutative rings

K. Suzuki
J. Algebra 175 (1995), 526–536. MR1339654 • 2007

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