[代數] 幾題有關order的問題

看板Math作者JoeMaddon (我是西瓜)時間12年前 (2011/12/06 11:56)推噓1(1推 0噓 5→)

留言6則, 4人參與討論串1/1

1.Recall the element @ is a group of G with identity element e has order r > 0 if a^r = e and no smaller positive power of @ is the identity. Concider the group S8. a.What is the order of the cycle (1,4,5,7)? b.State a theorem suggested by part (a) c.What is the order of # = (4,5)(2,3,7)? of $ = (1,4)(3,5,7,8)? d.Find the order of each of the permutations given in € =(1,8)(3,6,4)(5,7) $ =(1,3,4)(2,6)(5,8,7),& =(1,3,4,7,8,6,5,2) by looking at its decomposition into a product of disjoint cycles. e.State a theorem suggested by part(c) and (d).[hint:The imporrant words you are looking for are common mutiple.] -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 115.30.69.50

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Sfly

12/06 12:04, , 1^F

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JoeMaddon

12/06 12:23, , 2^F

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TRAP

12/06 19:48, , 3^F

12/06 19:48, 3^F