【摘要】 设K1和K2均为体,m和n为两个正整数,GLm(K1)和GLn(K2)分别表示K1上m阶一般线性群和K2上n阶一般线性群,映射f:GLm(K1)→GLn(K2)称为从GLm(K1)到GLn(K2)的群同态,如果f(AB)=f(A)f(B),A,B∈GLm(K1)。刻画了m>n时从GLm(K1)到GLn(K2)的所有群同态。更多还原

【Abstract】 Suppose K1 and K2 are division rings.For given two positive integers m and n,let GLm(K1) and GLn(K2) be the general linear groups of order m over K1 and order n over K2,respectively.A map f:GLm(K1)→GLn(K2) is called a group homomorphism if f(AB)=f(A)f(B) for any A,B∈GLm(K1).When m>n,all group homomorphisms from GLm(K1) to GLn(K2) are determined.更多还原