## 2015年6月26日金曜日

### 数学 - 群論 - 部分群と生成系(シンメトリー, 二面体群, 部分群, 正六角形)

• 数式入力ソフト(TeX, MathML): MathType
• MathML対応ブラウザ: Firefox、Safari
• MathML非対応ブラウザ(Internet Explorer, Google Chrome...)用JavaScript Library: MathJax

$\begin{array}{l}{D}_{6}=\left\{e,\sigma ,{\sigma }^{2},{\sigma }^{3},{\sigma }^{4},{\sigma }^{5},\mathfrak{r},\sigma \mathfrak{r},{\sigma }^{2}\mathfrak{r},{\sigma }^{3}\mathfrak{r},{\sigma }^{4}\mathfrak{r},{\sigma }^{5}\mathfrak{r}\right\}\\ \left\{e\right\}\\ \\ \left\{e,{\sigma }^{3}\right\}\\ \left\{e,\mathfrak{r}\right\}\\ \left\{e,\sigma \mathfrak{r}\right\}\\ \left\{e,{\sigma }^{2}\mathfrak{r}\right\}\\ \left\{e,{\sigma }^{3}\mathfrak{r}\right\}\\ \left\{e,{\sigma }^{4}\mathfrak{r}\right\}\\ \left\{e,{\sigma }^{5}\mathfrak{r}\right\}\\ \\ \left\{e,{\sigma }^{2},{\sigma }^{4}\right\}\\ \\ \left\{e,{\sigma }^{3},\mathfrak{r},{\sigma }^{3}\mathfrak{r}\right\}\\ \left\{e,{\sigma }^{3},\sigma \mathfrak{r},{\sigma }^{4}\mathfrak{r}\right\}\\ \left\{e,{\sigma }^{3},{\sigma }^{2}\mathfrak{r},{\sigma }^{5}\mathfrak{r}\right\}\\ \\ \left\{e,\sigma ,{\sigma }^{2},{\sigma }^{3},{\sigma }^{4},{\sigma }^{5}\right\}\\ \left\{e,{\sigma }^{2},{\sigma }^{4},\mathfrak{r},{\sigma }^{2}\mathfrak{r},{\sigma }^{4}\mathfrak{r}\right\}\\ \left\{e,{\sigma }^{2},{\sigma }^{4},\sigma \mathfrak{r},{\sigma }^{3}\mathfrak{r},{\sigma }^{5}\mathfrak{r}\right\}\\ \left\{e\right\}\\ \\ \left\{e,\sigma ,{\sigma }^{2},{\sigma }^{3},{\sigma }^{4},{\sigma }^{5},\sigma \mathfrak{r},{\sigma }^{2}\mathfrak{r},{\sigma }^{3}\mathfrak{r},{\sigma }^{4}\mathfrak{r},{\sigma }^{5}\mathfrak{r}\right\}\end{array}$