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.
%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
}