Finite Bruck loops
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- by Michael Aschbacher, Michael K. Kinyon and J. D. Phillips PDF
- Trans. Amer. Math. Soc. 358 (2006), 3061-3075 Request permission
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.References
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Additional Information
- Michael Aschbacher
- Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
- MR Author ID: 27630
- Michael K. Kinyon
- Affiliation: Department of Mathematical Sciences, Indiana University South Bend, South Bend, Indiana 46634
- MR Author ID: 267243
- ORCID: 0000-0002-5227-8632
- J. D. Phillips
- Affiliation: Department of Mathematics and Computer Science, Wabash College, Crawfordsville, Indiana 47933
- MR Author ID: 322053
- 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
- © Copyright 2005 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 358 (2006), 3061-3075
- MSC (2000): Primary 20N05
- DOI: https://doi.org/10.1090/S0002-9947-05-03778-5
- MathSciNet review: 2216258