96年 - 96 淡江大學轉學考代數#55974

科目：轉學考-代數 | 年份：96年 | 選擇題數：0 | 申論題數：7

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選擇題 (0)

申論題 (7)

1. Prove that {1,-1, i, -i} is a cyclic group under the usual multiplication. (10%)

2. Show that a group G is abelian if for each g in G g² = e, where e is the identity of G (15%)

3. Show that any group order 7 is cyclic. (15%)

4. Let G be a group such that 200 ＜ |G| ＜ 300. Suppose G has subgroups of order 21 and 33, find |G|. (15%)

【已刪除】5. Let R be a commutative ring with identity 1. Prove that an ideal P is a prime if and only if

is an integral domain. (15%)

6. Prove that Z is a PID, where Z is the set of integers. (15%)

7. Up to isomorphism, find all abelian groups of order 12. (15%)