三维空间子群网的推导  

Derivation of subgroup network of three-dimensional crystallographic symmetry group

作　　者：叶笑蓉[1] 曹佑安[2] 袁鸿武[2] 杨奇斌[1] 王元明[3] 

机构地区：[1]湘潭大学物理系,湘潭411105 [2]湘潭大学数学系,湘潭411105 [3]中国科学院沈阳金属研究所,沈阳110015

出　　处：《物理学报》2002年第5期1087-1093,共7页Acta Physica Sinica

基　　金：国家自然科学基金 (批准号 :10 0 740 5 2 );湖南省教育厅基金 (批准号 99C10 3和 0 1A0 0 3)资助的课题~~

摘　　要：在严格的群论基础上对三维空间的两个几何不等价的极大有限群的子群网进行了详细推导 .首先对两个极大有限群的所有对称操作矩阵的几何意义进行了逐一分析 ,然后根据群和子群的关系找出了它们所包含的全部子群 。The subgroup network of the three-dimensional crystallographic symmetry group has been derived based on the two maximal finite groups corresponding to two geometrically inequivalent classes. First, the geometrical meaning of every group element of these two maximal finite groups was analysed, then all the subgroups of them was derived according to the relationship between supergroup and subgroup. Tire advantages of algebraic crystallography based on quadratic form theory were discussed.

关 键 词：二次型 同构 等价类 群论 有限群 对称变换 晶体学 矩阵 三维空间 子群网 

分 类 号：O711[理学—晶体学] O152