QUIPU: DECORATED PERMUTATION REPRESENTATIONS FINITE GROUPS

This book studies dihedral groups, dicyclic groups, other finite subgroups of the 3-dimensional sphere, and the 2-fold extensions of the symmetric group on 4 letters from the point of view of decorated string diagrams of permutations. These are our metaphorical quipu. As you might expect, the book is replete with illustrations. In (almost) all cases, explicit diagrams for the elements of the group are given. The exception is the binary icosahedral group in which only the generators and relations are exhibited.

Contents:
IntroductionBackground and Motivating ExamplesMatrix DescriptionsThe 3-Dimensional Sphere is a GroupExtensions of the Permutation Group Σ4The Binary Tetrahedral GroupThe Binary Icosahedral GroupComputing Group 2-Cocycles
Readership: Advanced undergraduates, beginning graduate students in mathematics, mathematical hobbyists, visual learners, young physicists.

Key Features: A gentle and accessible introduction to abstract algebra with a novel diagrammatic approach Many visualizations and diagrams The diagrammatic approach, interrelating algebra and geometry/topology, may be useful for researchers as well, in particular those working in topology and physics