The $27$-dimensional module for $E_ 6$. III
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- by Michael Aschbacher PDF
- Trans. Amer. Math. Soc. 321 (1990), 45-84 Request permission
Abstract:
This is the third in a series of five papers investigating the subgroup structure of the universal Chevalley group $G = {E_6}(F)$ of type ${E_6}$ over a field $F$ and the geometry induced on the $27$-dimensional $FG$-module $V$ by the symmetric trilinear form $f$ preserved by $G$. The series uses the geometry on $V$ to describe and enumerate (up to a small list of ambiguities) all closed maximal subgroups of $G$ when $F$ is finite or algebraically closed.References
- Michael Aschbacher, The $27$-dimensional module for $E_6$. I, Invent. Math. 89 (1987), no.Β 1, 159β195. MR 892190, DOI 10.1007/BF01404676
- Michael Aschbacher, Chevalley groups of type $G_2$ as the group of a trilinear form, J. Algebra 109 (1987), no.Β 1, 193β259. MR 898346, DOI 10.1016/0021-8693(87)90173-6
- Michael Aschbacher, Some multilinear forms with large isometry groups, Geom. Dedicata 25 (1988), no.Β 1-3, 417β465. Geometries and groups (Noordwijkerhout, 1986). MR 925846, DOI 10.1007/BF00191936
- Roger W. Carter, Finite groups of Lie type, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1985. Conjugacy classes and complex characters; A Wiley-Interscience Publication. MR 794307
- J.-P. Serre, A course in arithmetic, Graduate Texts in Mathematics, No. 7, Springer-Verlag, New York-Heidelberg, 1973. Translated from the French. MR 0344216, DOI 10.1007/978-1-4684-9884-4
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 321 (1990), 45-84
- MSC: Primary 20F29; Secondary 20E15
- DOI: https://doi.org/10.1090/S0002-9947-1990-0986684-6
- MathSciNet review: 986684