We show that the lower bounds for Betti numbers given in (J. Pure Appl. Algebra 157 (2001) 135) are equalities for a class of racks that includes dihedral and Alexander racks. We confirm a conjecture from the same paper by defining a splitting for the short exact sequence of quandle chain complexes. We define isomorphisms between Alexander racks of certain forms, and we also list the second and third homology groups of some dihedral and Alexander quandles. © 2002 Elsevier Science B.V. All rights reserved.
Publication Source (Journal or Book title)
Journal of Pure and Applied Algebra
Litherland, R., & Nelson, S. (2003). The Betti numbers of some finite racks. Journal of Pure and Applied Algebra, 178 (2), 187-202. https://doi.org/10.1016/S0022-4049(02)00211-6