Dihedralizing the quaternions

2023/10/19 by Matthew Macauley, Macauley, Matthew
Engineering · Mathematics · #05C25 #20D99 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #History and Overview (math.HO) #Mathematics and Applications #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2310.13087

openalex publication_date 2023/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we take the classic dihedral and quaternion groups and explore questions like "what if we replace i=e^2πi/4 in Q₈ with a larger root of unity?" and "what if we add a reflection to Q₈?" The delightful answers reveal lesser-known families like the dicyclic, diquaternion, semidihedral, and semiabelian groups, which come to life with visuals such as Cayley graphs, cycle graphs, and subgroup lattices.

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