%0 Generic %1 Ehrman2005a %A Ehrman, G. %A Gurpinar, A. %A Thibault, M. %A Yetter, D. N. %D 2005 %K algebra quandles %T Toward a classification of finite quandles %U http://arxiv.org/abs/math/0512135 %X This paper summarizes substantive new results derived by a student team (the first three authors) under the direction of the fourth author at the 2005 session of the KSU REU ``Brainstorming and Barnstorming''. The main results are a decomposition theorem for quandles in terms of an operation of `semidisjoint union' showing that all finite quandles canonically decompose via iterated semidisjoint unions into connected subquandles, and a structure theorem for finite connected quandles with prescribe inner automorphism group. The latter theorem suggests a new approach to the classification of finite connected quandles.

@misc{Ehrman2005a, abstract = { This paper summarizes substantive new results derived by a student team (the first three authors) under the direction of the fourth author at the 2005 session of the KSU REU ``Brainstorming and Barnstorming''. The main results are a decomposition theorem for quandles in terms of an operation of `semidisjoint union' showing that all finite quandles canonically decompose via iterated semidisjoint unions into connected subquandles, and a structure theorem for finite connected quandles with prescribe inner automorphism group. The latter theorem suggests a new approach to the classification of finite connected quandles. }, added-at = {2009-05-22T15:50:38.000+0200}, author = {Ehrman, G. and Gurpinar, A. and Thibault, M. and Yetter, D. N.}, biburl = {https://www.bibsonomy.org/bibtex/246824ee7aa5487fed974499209d6bea3/njj}, description = {Toward a classification of finite quandles}, interhash = {74eeba8c1646009a238fa655d69c0941}, intrahash = {46824ee7aa5487fed974499209d6bea3}, keywords = {algebra quandles}, note = {cite arxiv:math/0512135 Comment: 12 pages LaTeX}, timestamp = {2009-05-22T15:50:38.000+0200}, title = {Toward a classification of finite quandles}, url = {http://arxiv.org/abs/math/0512135}, year = 2005 }