LAUSR

In this paper, we obtain the factorization of direct production and order of group GL(n, Zm) in a simple method. Then we generalize some properties of GL(2, Zp) proposed by Huppert, and prove that the group $$GL\left( {2,{Z_{{z^\lambda }}}} \right)$$GL(2,Zzλ) is solvable. We also prove that group GL(n, Zp) is solvable if and only if GL(n, Zp) is solvable, and list the generators of groups GL(n, Zp) and SL(n, Zp). At last, we prove that PSL(2, Zp)(p > 3) and PSL(n, Zp)(n > 3) are simple.