# ALEXANDER QUANDLES OF ORDER 16

@article{Murillo2004ALEXANDERQO,
title={ALEXANDER QUANDLES OF ORDER 16},
author={Gabriel Murillo and Sam Nelson},
journal={Journal of Knot Theory and Its Ramifications},
year={2004},
volume={17},
pages={273-278}
}
• Published 23 September 2004
• Mathematics
• Journal of Knot Theory and Its Ramifications
Isomorphism classes of Alexander quandles of order 16 are determined, and classes of connected quandles are identified. This paper extends the list of distinct connected finite Alexander quandles.

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## References

SHOWING 1-4 OF 4 REFERENCES
State-sum invariants of knotted curves and surfaces from quandle cohomology
• Mathematics
• 1999
State-sum invariants for classical knots and knotted surfaces in 4-space are developed via the cohomology theory of quandles. Cohomology groups of quandles are computed to evaluate the invariants.
Classification of Finite Alexander Quandles
Two finite Alexander quandles with the same number of elements are isomorphic iff their Z[t,t^-1]-submodules Im(1-t) are isomorphic as modules. This yields specific conditions on when Alexander
Figure 3: Results of computation of Im(Id − φ) for Alexander quandles given by automorphisms
• Figure 3: Results of computation of Im(Id − φ) for Alexander quandles given by automorphisms