Find the subgroup of the following group?
1. G = < Z16, + >
2. G = < Z23, + >
3. G = < Z16*, X >
4. G = < Z17*, X >
Answers
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16
Answer:
Explanation:
h3i = {n · 3 ∈ Z18 | n ∈ Z} = {0, 3, 6, 9, 12, 15}
h15i = h−3i = {n·(−3) ∈ Z18 | n ∈ Z} = {n·3 ∈ Z18 | n ∈ Z} = h3i = {0, 3, 6, 9, 12, 15}
ha
3
i = {(a
3
)
n = a
3n ∈ hai | n ∈ Z} = {e, a3
, a6
, a9
, a12, a15}
ha
15i = ha
−3
i = ha
3
i = {e, a3
, a6
, a9
, a12, a15}
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