Connected Quandles and Transitive Groups

Authors

Alexander Hulpke, Colorado State University
David Stanovský, Charles University, University of Denver
Petr Vojtěchovský, University of DenverFollow

Publication Date

8-5-2015

Document Type

Article

Organizational Units

College of Natural Science and Mathematics, Mathematics

Keywords

Primary, 57M27, Secondary, 20N02, 20B10

Abstract

We establish a canonical correspondence between connected quandles and certain configurations in transitive groups, called quandle envelopes. This correspondence allows us to efficiently enumerate connected quandles of small orders, and present new proofs concerning connected quandles of order p and 2p. We also present a new characterization of connected quandles that are affine.

Publication Statement

Copyright held by author or publisher. User is responsible for all copyright compliance.

Recommended Citation

Hulpke, Alexander, et al. “Connected Quandles and Transitive Groups.” Journal of Pure and Applied Algebra, vol. 220, no. 2, 2016, pp. 735–758. doi: 10.1016/j.jpaa.2015.07.014.