Let G be the symmetric group S5. Can you find a cyclic subgroup of G of order(i) 1 (ii) 2 (iii) 3 (iv) 4 (v) 5 (vi) 6 (vii) 7?

Question

Let G be the symmetric group S5. Can you find a cyclic subgroup of G of order(i) 1 (ii) 2 (iii) 3 (iv) 4 (v) 5 (vi) 6 (vii) 7?
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Solution 1

Sure, let's find the cyclic subgroups of the symmetric group S5 of the given orders.

(i) The cyclic subgroup of order 1 is the trivial group {e}, where e is the identity element.

(ii) The cyclic subgroup of order 2 can be generated by a 2-cycle. For example, the subgroup generated by (12) is {(12) Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

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Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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