It is often very difficult to identify the structure of the automorphismgroup and the inner automorphismgroupof a group, and there is no general theory and method.
确定一个群的自同构群和内自同构群的结构往往十分困难，还没有一般性的理论及方法。
2
The outer automorphismgroupof the free product of two cyclic groups is constructed, and two exact formulas for calculating its order are established.
具体地构造出两个有限循环群的自由积的外自同构群，并给出了其阶的计算公式。
3
Under this assumption, the present paper further gives a characterization for the automorphismgroupof C( G, S) in terms of the quotient di-graph and the kernel K.