2015/01/06 by Logan Crew, Crew, Logan · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems #math.GR
paper · pdf · doi:10.48550/arxiv.1501.03170
Undergraduate Honors Thesis in Mathematics
arxiv created 2015/01/06 · openalex publication_date 2015/01/06 · arxiv updated 2015/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
One of the classical problems in group theory is determining the set of positive integers n such that every group of order n has a particular property P, such as cyclic or abelian. We first present the Sylow theorems and the idea of solvable groups, both of which will be invaluable in our analysis. We then gather various solutions to this problem for cyclic, abelian, nilpotent, and supersolvable groups, as well as groups with ordered Sylow towers. This work is an exposition of known results, but it is hoped that the reader will find useful the presentation in a single account of the various tools that have been used to solve this general problem. This article claims no originality, but is meant as a synthesis of related knowledge and resources.