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    Odd Order and Cyclic Groups

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    Suppose that G is a finite group of odd order 2n + 1. Prove or disprove that the number of cyclic subgroups of G is at most n + 1.

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    Solution Preview

    The statement is true.


    We know, each element g in G can generate a cyclic group <g>. So if the order of G is 2n+1, G contains at most 2n+1 cyclic subgroups. Now we want to show that G contains at most n+1 ...

    Solution Summary

    In this solution, the concepts of odd order and cyclic groups are investigated. The solution is detailed and well presented.