Posted by haifeng on 2022-10-16 21:56:23 last update 2022-10-16 21:56:23 | Answers (0) | 收藏
$S_4$ 是四个元素的对称群, 其阶为 $|S_4|=4!=24$,
subgroups of S_4 (planetmath.org)
abstract algebra - $D_8$ as a derived subgroup - Mathematics Stack Exchange
Posted by haifeng on 2011-08-19 08:21:41 last update 2011-08-19 10:58:53 | Answers (0) | 收藏
假设 $\Gamma_i=(X_i,\circ^i),\ i=1,2,\ldots,n$ 是 $n$ 个有限群, $\circ^i$ 是第 $i$ 个有限群的乘法. 它们的笛卡尔乘积定义为 $\Gamma=(X_1\times X_2\times\cdots\times X_n,\circ)$, 其中运算 $\circ$ 定义为
\[ (x_1,x_2,\ldots,x_n)\circ(y_1,y_2,\ldots,y_n)=(x_1\circ^1 y_1,x_2\circ^2 y_2,\ldots,x_n\circ^n y_n), \]容易验证, 该定义是合理的.
Posted by haifeng on 2011-08-17 14:36:51 last update 2011-08-17 14:36:51 | Answers (0) | 收藏
Posted by haifeng on 2011-08-14 17:01:41 last update 2011-08-14 17:01:41 | Answers (0) | 收藏
设 $G$ 由 $x,y$ 两个元素生成的有限群, 且满足下述关系
\[ x^3=y^2=e,\quad xy=yx^2, \]请写出这个群.
Posted by haifeng on 2011-08-14 16:27:25 last update 2011-08-14 16:27:25 | Answers (1) | 收藏
Posted by haifeng on 2011-08-14 16:06:45 last update 2011-08-14 16:53:27 | Answers (0) | 收藏
Posted by haifeng on 2011-08-10 10:35:38 last update 2011-08-10 10:35:38 | Answers (0) | 收藏
Posted by haifeng on 2011-08-09 15:41:03 last update 2011-08-09 15:41:54 | Answers (0) | 收藏
Posted by haifeng on 2011-08-09 15:13:30 last update 2018-10-30 14:45:52 | Answers (1) | 收藏
[提示] 证明 $N$ 必为特征单群, 然后利用定理: 有限特征单群 $G$ 是同构单群的直积
Posted by haifeng on 2011-08-08 15:49:02 last update 2011-08-08 15:49:02 | Answers (0) | 收藏