# Odd Order and Cyclic Groups

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.

Proof:

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.

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