Quipu: Decorated Permutation Representations Of 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.

Professor Yongju Bae is a faculty member at Kyungpook National University. He has served as Dean of Admissions. He has published 35 research papers with focuses upon algebraic aspects of knot theory that includes recent work on the structure of quandles. He has lectured in Korea, Japan, Russia, the United States, and the United Kingdom. He enjoys playing tennis. He is a proud father and grandfather.

Dr Byeorhi Kim is one of several recent PhDs who earned her degree under the direction of Professor Bae. She is currently working as a post-doctoral researcher at Pohang University of Science and Technology. Her research interests include 2-dimensional surfaces in 4-manifolds and quandle structures related to knot theory. Even in her short career, she has attended conferences and lectured in England, the United States, Korea, Japan, and China. Her cat enjoys helping her with her mathematical research.

J Scott Carter is a Professor Emeritus from the University of South Alabama where he served for 29 years. He has published 84 works that include two prior books with World Science Publishing. In addition to developing mathematical illustrations that, he hopes, enhance our understanding of the mathematical world, he enjoys walking, biking, and swimming as well as playing guitar. He is a proud father of three boys.