子群

The group of even numbers forms a subgroup within the integers.
这个偶数集合在整数中构成一个子群。
The symmetric group S3 is a subgroup of the permutation group on three elements.
对称群S3是三个元素排列群的一个子群。
The set of invertible 2x2 matrices forms a subgroup under matrix multiplication.
可逆的2x2矩阵集合在矩阵乘法下构成一个子群。
In a group G, the identity element {e} and the set of all its inverses form a subgroup called the center.
在群G中，单位元和所有其逆元构成的集合称为中心，这是一个子群。
The normal subgroup H of G is a subset that is closed under both left and right multiplication by elements of G.
群G的正规子群H是一个在G的左乘和右乘下封闭的子集。
Every finite cyclic group is isomorphic to a subgroup of the integers under addition.
每个有限循环群都同构于整数加法下的一个子群。
The alternating group A4 is a subgroup of the symmetric group S4."
变换群A4是置换群S4的一个子群。
A subgroup can be trivial (containing only the identity) or non-trivial (containing more than one element)."
子群可以是平凡的（只包含单位元）或非平凡的（包含不止一个元素）。
A subgroup H of a group G is called a proper subgroup if it is not equal to G itself.
如果一个子群H不等于群G本身，则称H为G的一个真子群。
The intersection of two subgroups is also a subgroup.
两个子群的交集也是一个子群。