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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Every diassociative A-loop is Moufang


Authors: Michael K. Kinyon, Kenneth Kunen and J. D. Phillips
Journal: Proc. Amer. Math. Soc. 130 (2002), 619-624
MSC (2000): Primary 20N05; Secondary 68T15
Published electronically: June 19, 2001
MathSciNet review: 1866009
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Abstract:

An A-loop is a loop in which every inner mapping is an automorphism. A problem which had been open since 1956 is settled by showing that every diassociative A-loop is Moufang.


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Additional Information

Michael K. Kinyon
Affiliation: Department of Mathematics & Computer Science, Indiana University, South Bend, Indiana 46634
Address at time of publication: Department of Mathematics, Western Michigan University, Kalamazoo, Michigan 49008-5248
Email: mkinyon@iusb.edu

Kenneth Kunen
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 57306
Email: kunen@math.wisc.edu

J. D. Phillips
Affiliation: Department of Mathematics, Saint Mary’s College of California, Moraga, California 94575
Address at time of publication: Department of Mathematics and Computer Science, Wabash College, Crawfordsville, Indiana 47933
Email: phillips@stmarys-ca.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06090-7
PII: S 0002-9939(01)06090-7
Keywords: Diassociative loop, A-loop, Moufang loop
Received by editor(s): August 3, 2000
Received by editor(s) in revised form: August 18, 2000
Published electronically: June 19, 2001
Additional Notes: The second author was partially supported by NSF Grant DMS-9704520.
Communicated by: Lance W. Small
Article copyright: © Copyright 2001 American Mathematical Society