Subring subgroups in Chevalley groups with doubly laced root systems

JOURNAL OF ALGEBRA

卷:362

Article

Stepanov, Alexei^1,2 

[1] St Petersburg State Univ, Dept Math & Mech, St Petersburg, Russia

[2] Govt Coll Univ, Abdus Salam Sch Math Sci, Lahore, Pakistan

关键词: Chevalley groups;    Lattice of subgroups;    Group identity with constants;    Small semisimple element;   

DOI  :  10.1016/j.jalgebra.2012.04.007

来源: Elsevier

【 摘 要 】

We study the lattice E of subgroups of a Chevalley group G(Phi, A) over a ring A. containing its elementary subgroup E(Phi, S) over a subring S subset of A. The standard description asserts that for any H is an element of L there exists a unique subring R superset of S of A such that H contains E(Phi, R) as a normal subgroup. The standard description was obtained by Ya. Nuzhin for algebraic field extensions. On the other hand, it was expected that the standard description does not hold for transcendental extensions. This was recently proved by the author for simply laced root systems. Now, suppose that Phi is doubly laced, i.e. Phi = B-1, C-1 or F-4, and that 2 is invertible in S. In the article we prove that in these settings the standard description of L holds for an arbitrary pair of rings S subset of A. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free