Aschbacher, Michael and Kinyon, Michael K. and Phillips, J. D. (2006) Finite Bruck loops. Transactions of the American Mathematical Society, 358 (7). pp. 3061-3075. ISSN 0002-9947. doi:10.1090/S0002-9947-05-03778-5. https://resolver.caltech.edu/CaltechAUTHORS:20110209-094820472
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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.
| Item Type: | Article | |||||||||
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| Additional Information: | © 2005 American Mathematical Society. Received by the editors December 15, 2003 and, in revised form, June 29, 2004. Article electronically published on September 22, 2005. The first author was partially supported by NSF-0203417. | |||||||||
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| Issue or Number: | 7 | |||||||||
| Classification Code: | 2000 Mathematics Subject Classification: Primary 20N05 | |||||||||
| DOI: | 10.1090/S0002-9947-05-03778-5 | |||||||||
| Record Number: | CaltechAUTHORS:20110209-094820472 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20110209-094820472 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 22090 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 10 Mar 2011 23:42 | |||||||||
| Last Modified: | 09 Nov 2021 16:02 |
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