## A Classification of Integers n for Which the Only Groups of Order n are Cyclic (Pt. II)

**Point of Post: **This is a continuation of this post.

## A Classification of Integers n for Which the Only Groups of Order n are Cyclic (Pt. I)

**Point of Post:** In this post we conglomerate and extend a few exercises in Dummit and Foote’s *Abstract Algebra *which will prove that the only positive integers for which the only group (up to isomorphism) of order is are integers of the form are distinct primes with for any .

*Motivation*

This post will complete several lemmas/theorems* *which works towards proving not only that every group of order where for any (greatly generalizing the statement that a group of for primes with is cyclic) but also that numbers of this form are the only numbers for which the converse is true (namely every group of order is cyclic).