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Finite Bruck loops

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.

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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:© 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
Record Number:CaltechAUTHORS:20110209-094820472
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:22090
Deposited By: Tony Diaz
Deposited On:10 Mar 2011 23:42
Last Modified:09 Nov 2021 16:02

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