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
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Bruck loops are Bol loops satisfying the automorphic inverse property. We prove a structure theorem for finite Bruck loops 
, showing that 
is essentially the direct product of a Bruck loop of odd order with a 
-element Bruck loop. The former class of loops is well understood. We identify the minimal obstructions to the conjecture that all finite 
-element Bruck loops are 
-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
