摘要
Let L be a simple Lie algebra with irreducible root system. having roots of different length, F be a field of charaCteristic different from 2, G = L(F) be a Chevalley group of type L over F. Denote by Φl the set of all long roots in Φl Set Gl = <xr (t); f∈EΦl,t∈F>. It is a subgroup of G generated by all the long root subgroups. This paper determines the pronormality of Gl in G when L is not of type G2.
Let L be a simple Lie algebra with irreducible root system. having roots of different length, F be a field of charaCteristic different from 2, G = L(F) be a Chevalley group of type L over F. Denote by Φl the set of all long roots in Φl Set Gl = <xr (t); f∈EΦl,t∈F>. It is a subgroup of G generated by all the long root subgroups. This paper determines the pronormality of Gl in G when L is not of type G2.
基金
Project supported by the National Natural Science Foundation of China (No.19671079).
关键词
预正规子群
李代数
谢瓦莱群
根系
Chevalley groups, Root systems, Pronormal subgroups
