有限局部环上酉群的Sylow子群  

Sylow Subgroups of Unitary Groups over Finite Local Rings

作　　者：高有[1] 王红丽[1] 

机构地区：[1]中国民航大学理学院,天津300300

出　　处：《中国民航大学学报》2007年第5期57-60,共4页Journal of Civil Aviation University of China

基　　金：天津市自然科学基金项目

摘　　要：设K=Fq2,其特征为p,q=pα,K有对合自同构:ωa|→aq,G是一个p-群,其阶为p,β群代数R=KG为一局部环。本文给出了R=KG上酉群U2nR的Sylow子群,若charK=p,U2nR的Sylow p-子群同构于某些特殊形式的矩阵生成的子群;若charK=p≠l,U2nR的Sylow l-子群同构于一循环群或半二面体群与若干Zl型循环群的圈积。Let K=Fq^2,with charK=p where q=p^α,define an involutive automorphism of K by ω：a｜→a^q,G is a p-group of order p^β,group algebra R=KG is a local ring. In this paper,determine the Sylow subgroups of unitary groups U2nR over R=KG. If charK=p ,the Sylow p-subgroups of U2nR are isomorphic to the subgroups generated by some special formal matrices;If charK=p ≠l,Sylow l-subgroups of U2nR are isomorphic to a cyclic group or the wreath product of a semidihedral group and several Z1 type cyclic groups.

关 键 词：局部环 酉群 SYLOW子群 

分 类 号：O152.1[理学—数学]