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.
|Number of pages||16|
|Journal||Communications in Algebra|
|Early online date||1 Jan 2003|
|Publication status||Published - 1 Jan 2003|