The structure of symplectic groups over arbitrary commutative rings |
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Authors: | Li Fuan |
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Affiliation: | (1) Institute of Mathematics, Academia Sinica, China |
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Abstract: | LetR be an arbitrary commutative ring, andn be an integer ≥3. It is proved for any idealJ ofR thatESp 2n(R,J)=[ESp 2n(R),ESp 2n(J)]=[ESp 2n(R),ESp 2n(R,J)] =[ESp 2n(R),GSp 2n(R,J)]=[Sp 2n(R),ESp 2n(R,J)]. Furthermore, the problem of normal subgroups ofSp 2n(R) has an affirmative solution if and only ifaR=a 2R+2aR for eacha inR. This covers the relevant results of [4], [8], [10], [12] and [13]. Project Supported by the Science Fund of the Chinese Academy of Sciences |
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