Connected quandles and transitive groups
  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. 
Alexander Hulpke, David Stanovsk\'y, Petr Vojt\v{e}chovsk\'y
math.GR math.GT