Canonical Forms for Operation Tables of Finite Connected Quandles |
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Authors: | Chuichiro Hayashi |
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Institution: | 1. Department of Mathematical and Physical Sciences, Faculty of Science , Japan Women's University, Mejirodai, Bunkyo-ku , Tokyo , Japan hayashic@fc.jwu.ac.jp |
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Abstract: | We introduce a notion of natural orderings of elements of connected finite quandles. Let Q be such a quandle of order n. Any automophism on Q is a natural ordering when the elements are already ordered naturally. Suppose that the permutation *q is a cycle of length n ? 1. Then, the operation tables for such orderings coincide, which leads to the classification of automorphisms on Q. Moreover, every row and column of the operation table contains all the elements of such a quandle, which is due to K. Oshiro. We also consider the general case of finite connected quandles. |
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Keywords: | Canonical form for operation table Finite connected quandle |
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