文章目录
- 前言
- 一、证明命题6.6
- 二、证明命题6.7
- 三、证明对任意偶数阶群G，都存在g ∈ \in ∈,g ≠ \neq =e且 g 2 g^2 g2=e
- 四、给出命题6.9的完整证明
- 五、设G是群，对任意n ∈ \in ∈N,i ∈ \in ∈ [ 0 , n ] [0,n] [0,n], g i g_i gi ∈ \in ∈G。证明 g 0 g_0 g0 g 1 g_1 g1 ⋅ \cdot ⋅ ⋅ \cdot ⋅ ⋅ \cdot ⋅ g n g_n gn的逆元是 g n − 1 g_n^{-1} gn−1 ⋅ \cdot ⋅ ⋅ \cdot ⋅ ⋅ \cdot ⋅ g 1 − 1 g_1^{-1} g1−1 g 0 − 1 g_0^{-1} g0−1。
前言
一、证明命题6.6
二、证明命题6.7
三、证明对任意偶数阶群G，都存在g ∈ \in ∈,g ≠ \neq =e且 g 2 g^2 g2=e
四、给出命题6.9的完整证明
五、设G是群，对任意n ∈ \in ∈N,i ∈ \in ∈ [ 0 , n ] [0,n] [0,n], g i g_i gi ∈ \in ∈G。证明 g 0 g_0 g0 g 1 g_1 g1 ⋅ \cdot ⋅ ⋅ \cdot ⋅ ⋅ \cdot ⋅ g n g_n gn的逆元是 g n − 1 g_n^{-1} gn−1 ⋅ \cdot ⋅ ⋅ \cdot ⋅ ⋅ \cdot ⋅ g 1 − 1 g_1^{-1} g1−1 g 0 − 1 g_0^{-1} g0−1。
