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Order and Number of Cyclic Subgroups

Please address the following question by answering the following:
Suppose that G is a finite group of even order 2n.
Prove or disprove that the number of cyclic subgroups of G is at most n + 2.

Solution Preview

The statement is false. Here is a counterexample.
We consider the additive group G=Z2*Z2*Z2, where Z2={0,1}. Each ...

Solution Summary

In this solution, a brief, but straight-forward response is used to address this math based problem, focused on subgroups.