Abstract
Taking G to be a Chevalley group of rank at least 3 and U to be the unipotent radical of a Borel subgroup B, an extremal subgroup, A is an abelian normal subgroup of U which is not contained in the intersection of all the unipotent radicals of the rank 1 parabolic subgroups of G containing B. If there is an unique rank 1 parabolic subgroup P of G containing B with the property that A is not contained in the unipotent radical of P, then A is called a unique node extremal subgroup. In this paper we investigate the embedding of unique node extremal subgroups in U and prove that, apart from some specified cases, such a subgroup is contained in the unipotent radical of a certain maximal parabolic subgroup.
Original language | English |
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Pages (from-to) | 3471-3486 |
Number of pages | 16 |
Journal | Communications in Algebra |
Volume | 31 |
Issue number | 7 |
Early online date | 1 Jan 2003 |
DOIs | |
Publication status | Published - 1 Jan 2003 |