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4. Calculate the order of the element 4 in group (Z*18, x mod 18) 5. Calculate the order of element 23 in a group (Z51, +) 6. Calculate the order of the element t12 in group (S3, o)

4. Calculate the order of the element 4 in group (Z*18, x mod 18) 5. Calculate the order of element 23 in a group (Z51, +) 6. Calculate the order of the element t12 in group (S3, o)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2.3 (Q4 to Q6 ) Please provide detailed solution with explanation and justification asap to get a upvote for Q4 to onwards 6 three parts
2.3 Cyclic group, order of a group/element 1. Write a definition of a cyclic group. Provide two examples of cyclic group. 2. Calculate the order of the symmetric group S8 3. Calculate the order of the group (Z7, +) 4. Calculate the order of the element 4 in group (Z*18, × mod 18) 5. Calculate the order of element 23 in a group (Z51, +) 6. Calculate the order of the element t12 in group (S3, o)
Transcribed Image Text:2.3 Cyclic group, order of a group/element 1. Write a definition of a cyclic group. Provide two examples of cyclic group. 2. Calculate the order of the symmetric group S8 3. Calculate the order of the group (Z7, +) 4. Calculate the order of the element 4 in group (Z*18, × mod 18) 5. Calculate the order of element 23 in a group (Z51, +) 6. Calculate the order of the element t12 in group (S3, o)
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