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.© BrainMass Inc. brainmass.com July 16, 2018, 8:45 am ad1c9bdddf
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 ...
In this solution, the concepts of odd order and cyclic groups are investigated. The solution is detailed and well presented.