[代數] 請教一題normal subgroup

看板Math作者 (小蘿莉銀行)時間15年前 (2011/03/12 11:30), 編輯推噓1(102)
留言3則, 2人參與, 最新討論串1/1
(1)Show that the Klien group K={e,(1 2)(3 4),(1 3)(2 4),(1 4)(2 3)} is a normal subgroup of A_4 and S_4. (2)Show that K is a subgroup of A_5, but is not normal sublgroup of A_5. 謝謝 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 115.43.146.210

03/12 12:48, , 1F
K中除了e外都是兩個cycle相乘 用S_4的元素conjugate
03/12 12:48, 1F

03/12 12:49, , 2F
仍然是兩個cycle相乘 因此仍然屬於K 其餘類似
03/12 12:49, 2F

03/13 18:00, , 3F
感謝,我後來有做出來了!!!!
03/13 18:00, 3F
文章代碼(AID): #1DUkZLxE (Math)