Canonical forms for operation tables of finiate connected quandles

Details Canonical forms for operation tables of finiate connected quandles Canonical forms for operation tables of finiate connected quandles

2011-10-09

arxiv.org/abs/1110.1849v1

Mathematics

Group Theory

8 pages, 0 figures

Scientific paper

We introduce a notion of natural orderings of elements of finite connected quandles of order $n$. When the elements of such a quandle $Q$ are already ordered naturally, any automophism on $Q$ is a natural ordering. Although there are many natural orderings, the operation tables for such orderings coincide when the permutation $*q$ is a cycle of length $n-1$. This leads to the classification of automorphisms on such a quandle. Moreover, it is also shown that every row and column of the operation table of such a quandle contains all the elements of $Q$, which is due to K. Oshiro. We also consider the general case of finite connected quandles.

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