最后确定了W及其泛中心扩张的自同构群的结构。
Finally, the structures of the automorphism groups of W and its universal central extension are characterized.
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。
The outer automorphism group of the free product of two cyclic groups is constructed, and two exact formulas for calculating its order are established.
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。
It is often very difficult to identify the structure of the automorphism group and the inner automorphism group of a group, and there is no general theory and method.
如果一个圈与某个群同痕，那么它与此群同构，因此也为一个群。
If a loop is isotopic to a group, then it is isomorphic to that group and thus is itself a group.
继太古代胶东群形成之后的胶东事件，在胶东群中造成了第一期的南北向构造和同构造麻粒岩相高级区域变质。
The Jiaodong event, which took place after formation of the Archaean Jiaodong Group, caused the first phase of N-S structures and syntectonic granulite facies metamorphism.
运用基础代数中有关自同构、左平移、正规子群等理论，对群G的全形进行了简单的探讨，证明了几个有关的结论。
By using the theories in basic algebra about automorphism, left translation and normal subgroup, in the holomorph of G is discussed briefly, and several related conclusions are obtained.
沂蒙作家群的创作形成了思想意蕴的多倾向性共存，凝重的农民情结以及精神上与沂蒙文化的同构关系。
The works of Yimeng writers are a co-existential complex of multi-thought tendencies, including imposing countrymen complex and common spirits to Yimeng culture.
沂蒙作家群的创作形成了思想意蕴的多倾向性共存，凝重的农民情结以及精神上与沂蒙文化的同构关系。
The works of Yimeng writers are a co-existential complex of multi-thought tendencies, including imposing countrymen complex and common spirits to Yimeng culture.
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