奇异伪辛群的Carter子群

CARTER SUBGROUPS OF SINGULAR PSEUDO-SYMPLECTIC GROUPS

设 Fq是特征为 2的有限域 ,本文研究了 Fq上 2 ν+δ+t级奇异伪辛群 Ps2ν+δ+ t(Fq) (δ=1或 2 )的 Carter子群的存在性及结构 .得到的结果为 :若 q>2 ,Ps2ν+δ+ t(Fq)中不含 Carter子群 ,若 q=2 ,Ps2ν+δ+ t(Fq)的 Carter子群为它的 Sylow2 -子群的正规化子 .

Let Fq be a finite field of characteristic 2.In the present paper,the existence and structure of Carter subgroups of degree 2ν+δ+t of singular pseudo symplectic group Ps 2ν+δ+t (Fq)(δ=1 or 2) over Fq is showed.The main results are that if q>2,there exist no Carter subgroups in Ps 2ν+δ+t ;if q=2,Carter subgroups of Ps 2ν+δ+t (Fq) are normalizers of the Sylow 2\|subgroups of Ps 2ν+δ+t (Fq).