【摘 要】
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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. I
【机 构】
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Department of Applied MathematicsNorthwestern Polytechnical University, Xi’an, Shaanxi 710072, China
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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.
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