Hermitian Groups over Local Rings

• 来源期刊: 代数集刊（英文版）
• 学科: 数学
• 关键词: metabolic space hermitian group elementary hermitian group
• 年，卷（期）: 2001,（1）
• 页码范围: 1-10
• 页数: 10页
• 分类号: O1
• 语种: 英文

摘要

The general hermitian group GH2n(R,a1,... ,ar) of rank n and its elementary subgroup EH2n(R,a1,... ,ar) were introduced by Bak [1] and Tang [4], respectively. It is known that EH2n(R, a1,... , ar) is perfect whenever n ≥ r+ 3 and the stable elementary hermitian group EH(R,a1,... ,ar) is the commutator subgroup of the stable general hermitian group GH(R, a1,... , ar).In this paper, we prove that, when R is a local ring, EH2n(R, a1,... , ar) is a normal subgroup of GH2n (R, a1,... , ar) if n ≥ r+2, and is the commutator subgroup of GH2n(R, a1,... , ar) if n ≥ r + 3. In the special case that R is a division ring,we show that the quotient group of GH2n(R, a1,... , ar) by EH2n(R, a1,... , ar)is independent of the choice of a1,... , ar.