TY - JOUR
T1 - Unique node extremal subgroups
AU - Parker, Christopher
AU - Rowley, P
PY - 2003/1/1
Y1 - 2003/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0042974891&partnerID=8YFLogxK
U2 - 10.1081/AGB-120022235
DO - 10.1081/AGB-120022235
M3 - Article
SN - 1532-4125
SN - 1532-4125
SN - 1532-4125
SN - 1532-4125
SN - 1532-4125
SN - 1532-4125
VL - 31
SP - 3471
EP - 3486
JO - Communications in Algebra
JF - Communications in Algebra
IS - 7
ER -