有限交换环上典型群的Sylow子群

游宏

数学学报 ›› 1996, Vol. 39 ›› Issue (1) : 33-40.

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PDF(414 KB)
数学学报 ›› 1996, Vol. 39 ›› Issue (1) : 33-40. DOI: 10.12386/A1996sxxb0005
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有限交换环上典型群的Sylow子群

    游宏
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Sylow Subgroups of Classical Groups over Finite Commutative Rings

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摘要

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。

Abstract

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.

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Sylow子群 / 有限交换环 / 典型群

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游宏. 有限交换环上典型群的Sylow子群. 数学学报, 1996, 39(1): 33-40 https://doi.org/10.12386/A1996sxxb0005
Sylow Subgroups of Classical Groups over Finite Commutative Rings. Acta Mathematica Sinica, Chinese Series, 1996, 39(1): 33-40 https://doi.org/10.12386/A1996sxxb0005
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