基本解释：外自同构
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And their automorphism group sand outer automorphism groups are determined.对任意奇素数p,引入了一类所谓的算术p-群,并确定了其自同构群和外自同构群,所得结果推广具有一个循环极大子群的p-群的相应结论。
The outer automorphism group of the free product of two syclic 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。
A formula of the order of the outer automorphism group of a semidirect product is obtained,which can be applied to the investigation of the triviality of the outer automorphism group.设有限群 G=N H为半直积 ,本文借助于 N和 H的自同构求出了 G的外自同构群阶的公式 ,并给出了若干应用。
