If a loop is isotopic to a group, then it is isomorphic to that group and thus is itself a group. 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。
We generalize the infinitesimal transformations obtained in the Ernst fields of vacuum previously to the case including electromagnetic fields to form a larger infinite symmetric group which is isomorphic to the Virasoro group without a central term. 我们把以前在真空Ernst场中得到的无穷小对称变换推广到带电磁场的Ernst场中,得到了一个更大的无限维对称群,这个群与不带中心项的Virasoro群同构。
The hyperbolic complex space R_H is isomorphic to the 4-dimensional ( 4D) Minkowski spacetime, and the hyperbolic phase transformation group U_4 ( H) in R_H is just Lorentz transformation group on 4D relativistic spacetime. 双曲复空间RH同构于四维Minkowski时空,而其上的双曲相位变换群U4(H)就是四维相对论时空中的洛仑兹(Lorentz)变换群。
Prime Number and Two Isomorphic Group 素数与两个同构群
In this paper, from the six-term exact sequence, it is proved that the direct sum of Z and K1-group of a Toeplitz algebra is always isomorphic to the topological K1-group of the boundary of the relative domain. 本文通过六项正合列计算出,在强拟凸域上,它的拓扑边界上连续函数代数的K(1-)群同构于区域上Toeplitz代数的K1-群与Z的直和。
The method used can be generalized to prove that a linear space admitting a point-transitive automorphism group isomorphic to some almost simple group is not a projective plane. 本文对以下问题给出了一般方法:证明以某些几乎单群为点传递自同构群的线性空间不是射影平面。
The Isomorphic Theorem of Finite Abel Group 有限Abel群的同构定理
It is proved therefore that the lattice of group congruences on S is complete lattice isomorphic to the lattice of group congruences on I ( S), the inverse subsemigroup of principal elements of S. 在此基础上,证明了S的群同余格与S的由主元所组成的逆半群I(S)的群同余格完备格同构;
Based on the second isomorphic theorem and properties of the symmetric group, a theorem is proposed to construct one Sylow-p group of symmetric group by adding generators to p-group. 根据对称群的基本性质以及第二同构定理,给出了通过添加生成元到p群来构造对称群的一个Sylow-p子群的定理,添加的生成元保证能够快速得到对称群的一个Sylow-p子群。
C. Holland [ 1963] has proven that every lattice-ordered group is ( isomorphic to) a subgroup of the lattice-ordered group of all order-preserving permutations of a chain. So lattice-ordered permutation groups are important tools for describing the structure of lattice-ordered groups. W.C.Holland1963年证明了格序群可表示为某一全序集上的格序置换群[16],因此格序置换群是研究格序群的重要工具之一。
Every group is isomorphic image of some free group. 任何群都是自由群的同态像。