Steklov Institute of Mathematics at St.Petersburg

PREPRINT 10/2007

NORMAL STRUCTURE OF MAXIMAL PARABOLIC SUBGROUPS IN CHEVALLEY GROUPS OVER RINGS

This preprint was accepted October 9, 2007

ABSTRACT:
We study normal structure
of maximal parabolic subgroups of a Chevalley group over a
commutative ring. More precisely, we describe subgroups of a
maximal parabolic subgroup $P$ normalized by the elementary part
of its Levi subgroup. As a corollary we obtain a description of
subgroups in $P$ normalized by its elementary subgroup $EP$.