有限交换环上典型群的Sylow子群

令Ｒ为有限交换局部环，Ｍ表其唯一的极大理想，ｋ表其剩余类域．本文定出了Ｒ上的一般线性群ＧＬｎＲ，辛群Ｓｐ２ｎＲ及双曲正交群Ｏ２ｎＲ的Ｓｙｌｏｗ子群．一般讲，若ｃｈａｒｘ＝ｐ，上述三类典型群的Ｓｙｌｏｗ ｐ－子群分别同构于由某些特殊形式的矩阵生成的子群；若ｃｈａｒｋ≠ｐ，上述三类典型群的Ｓｙｌｏｗｐ－子群分别同构于一循环群或半二面体群与若干Ｚｐ型循环群的圈积。

Sylow Subgroups of Classical Groups over Finite Commutative Rings

Let R be a finite commutative local ring and let M denote the unique maximal ideal of R and k denote the residue field of R. In the present paper, the author determined the Sylow subgroups of the linear group GL.R, the symplectic group SP2nR and the hyperbolic orthogonal group O2nR. In general speaking, if chark = p, the Sylow p-subgroups of the three kinds of classical groups above are isomorphic to the subgroups generated by some special matrices respectively; if chark ≠ p, the Sylow p-subgroups of the three kinds of classical groups above are isomorphic to the wreath product of a cyclic group or a semidihedral group and finite terms of cyclic groups with type Zp.