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.
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