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94年 - 94 淡江大學 轉學考 代數#56429
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7. Show that any group oi'order 35 is eyclic.
其他申論題
3. Let G be a group such lhat | G | ＜ 200. Suppose G has subgroups of order 25 and 35, find the order of G.
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【已刪除】4. Let G be the set of ail rational numbers except -1. Show that (G, ) is a group, where ab = a + b + ab for all a and b in G.
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5. Let G = ＜a＞ be a cyclic group of order 30，where a is a generator of G. Determine ＜a5＞ and ＜a2＞.
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6. Up to isomorphism, Jind all groups of order 4.
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8. Find all distinct subgroups of Z l2.
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9. Prove that every ideal of the ring of integers is principal.
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10.Let G be a group and a and b are h G. Suppose a2 = e and ab4 a = b7. Show that b33 = e, where e is tlie identity of G.
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（一）10110111 是代表 10 進位多少的整數？【3 分】
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（二）4810轉為 8 位元格式是多少？【3 分】
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（三）這樣的表示法所能表達的整數範圍若以 10 進位表示，其起迄範圍為何？【4 分】 以上請列出計算過程。
#214344
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