4. (5 pt total) Let U denote the set of units of the field ?5. (a) List out the elements of U. (b) By a result we proved for homework, (U, ?) is a group (where ? is multiplication in ?5). Give the group table for (U, ?). (c) To what 'known' abelian group is (U, ?) isomorphic?
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The units are the elements that have a multiplicative inverse in the field. In Z5, the elements are {0, 1, 2, 3, 4}. We can exclude 0 because it does not have a multiplicative inverse. Now let's check the remaining elements: 1 * 1 = 1 (mod 5) 2 * 3 = 6 = 1 (mod Show more…
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