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 | 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