On The Direct Products Of Cyclic Groups And The Quotient Group ((?)_m×(?)_n)/N

The properties of a group can be studied by means of its equivalent group.However,for the general group,it is difficult to find a simple and concrete equivalent group.In this thesis,we respective consider when gcd(m,n)?1,m is a prime number and gcd(m,n)=1,we find equivalent group of quotient group((?)_m × (?)_n)/N,N is a normal subgroup.By means of the equivalence group of quotient group (?)_m × (?)_n,the number of subgroups and other properties of quotient group (?)_m × (?)_n are obtained.