群L(3,2)的GF(2)模分解

The Decomposability of L(3,2) Over GF(2) Modules

由于G=L(3,2) SL(3 2),所以L(3,2)中的元素可表示成GF(2)上的三阶矩阵.采用基本群论和矩阵的一些方法,讨论了群L(3,2)的GF(2)模分解,特别地,对于L(3,2)的GF(2)模的可分解性进行研究.考察了L(3,2)的GF(2)模可分解成不可约模的直和,若V为G的非凡模且t∈G,o(t)=2能使V/Cv(t)=2,则V=V1 V0,其中V1为G自然模,V0=CV(G);若V/CV(G)为G自然模,则V= A V0,其中 A为G不可约模, V/C V(G)为G自然模,且|C V(G)|≤2,V0≤CV(G).这些结论可用于Aamalgam问题的讨论,所使用的方法可以用于更为复杂的有限群的讨论.

By means of the group theroy and matrix theory,L(3,2)is regarted as matrix of three rank over GF(2) because of G=L(3,2)SL(3,2).This paper deals with the module L(3,2) over GF(2).The decomposability of L(3,2) over GF(2) modules is investigated in detail. If t∈G,o(t)=2 and V/Cv(t)=2,then V=V1V0,V0=Cv(G);If V/CV(G) is G natural module ,then V=V0,( is G irreducible module,/C(G) is G natural module,and |C(G)|≤2,V0≤CV(G).These results can be applied to the discussion of amalgam problem.The methods in this paper can be made use of in the discussion of module of finite groups.