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Normality in Elementary Subgroups of Chevalley Groups Over Rings

Published online by Cambridge University Press:  20 November 2018

James F. Hurley
James F. Hurley*
Affiliation:
The University of Connecticut, Storrs, Connecticut
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In [6] we have constructed certain normal subgroups G7 of the elementary subgroup GR of the Chevalley group G(L, R) over R corresponding to a finite dimensional simple Lie algebra L over the complex field, where R is a commutative ring with identity. The method employed was to augment somewhat the generators of the elementary subgroup EI of G corresponding to an ideal I of the underlying Chevalley algebra LR;EI is thus the group generated by all xr(t) in G having the property that ter ⊂ I. In [6, § 5] we noted that in general EI actually had to be enlarged for a normal subgroup of GR to be obtained.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 2 , 01 April 1976 , pp. 420 - 428
Copyright
Copyright © Canadian Mathematical Society 1976

References

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