Notes On Linear Group Of Degree Two

The general linear group and the special linear group are the basic of study in group theory,as well as extremely important classes of group.Through the discussion of many characters of them,we could obtain better proper methods to grasp the group theory in general.In this paper,we mainly give many conclusions in following.Let p be a prime number,1)The conjugate subgroup of UT2(Zpn)in SL2(Zpn) is the cyclic group2)When p=2and p=3, group M is the conjugate subgroup of UT2(Zpn)in GL2(Zpn) if and only if every element of M is the conjugate element of UT2(Zpn).3)When p=2and p=3,the Sylowp-subgroup of SL2(Zpn).