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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Finite Bruck loops


Authors: Michael Aschbacher, Michael K. Kinyon and J. D. Phillips
Journal: Trans. Amer. Math. Soc. 358 (2006), 3061-3075
MSC (2000): Primary 20N05
DOI: https://doi.org/10.1090/S0002-9947-05-03778-5
Published electronically: September 22, 2005
MathSciNet review: 2216258
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Abstract: Bruck loops are Bol loops satisfying the automorphic inverse property. We prove a structure theorem for finite Bruck loops $X$, showing that $X$ is essentially the direct product of a Bruck loop of odd order with a $2$-element Bruck loop. The former class of loops is well understood. We identify the minimal obstructions to the conjecture that all finite $2$-element Bruck loops are $2$-loops, leaving open the question of whether such obstructions actually exist.


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Additional Information

Michael Aschbacher
Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125

Michael K. Kinyon
Affiliation: Department of Mathematical Sciences, Indiana University South Bend, South Bend, Indiana 46634

J. D. Phillips
Affiliation: Department of Mathematics and Computer Science, Wabash College, Crawfordsville, Indiana 47933

DOI: https://doi.org/10.1090/S0002-9947-05-03778-5
Received by editor(s): December 15, 2003
Received by editor(s) in revised form: June 29, 2004
Published electronically: September 22, 2005
Additional Notes: The first author was partially supported by NSF-0203417
Article copyright: © Copyright 2005 American Mathematical Society