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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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.
Group Theory : Homomorphism, Subgroups, Abelian Groups and Group Order
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