Commutants of Bol loops of odd order
HTML articles powered by AMS MathViewer
- by Michael K. Kinyon and J. D. Phillips PDF
- Proc. Amer. Math. Soc. 132 (2004), 617-619 Request permission
Abstract:
In this note we show that the commutant of a Bol loop of odd order is a subloop.References
- Richard Hubert Bruck, A survey of binary systems, Reihe: Gruppentheorie, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1958. MR 0093552, DOI 10.1007/978-3-662-35338-7
- Stephen Doro, Simple Moufang loops, Math. Proc. Cambridge Philos. Soc. 83 (1978), no. 3, 377–392. MR 492031, DOI 10.1017/S0305004100054669
- T. Foguel, M. K. Kinyon, and J. D. Phillips, Bol loops and twisted subgroups of odd order, submitted.
- George Glauberman, On loops of odd order, J. Algebra 1 (1964), 374–396. MR 175991, DOI 10.1016/0021-8693(64)90017-1
- G. E. Moorhouse, Bol loops of order $16$, at URL: http://math.uwyo.edu/~moorhous/pub/bol/bol16.html.
- Hala O. Pflugfelder, Quasigroups and loops: introduction, Sigma Series in Pure Mathematics, vol. 7, Heldermann Verlag, Berlin, 1990. MR 1125767
- W. W. McCune, OTTER 3.0 Reference Manual and Guide, Technical Report ANL-94/6, Argonne National Laboratory, 1994, or see the URL: http://www-fp.mcs.anl.gov/division/software/
- D. A. Robinson, Bol loops, Trans. Amer. Math. Soc. 123 (1966), 341–354. MR 194545, DOI 10.1090/S0002-9947-1966-0194545-4
Additional Information
- Michael K. Kinyon
- Affiliation: Department of Mathematical Sciences, Indiana University South Bend, South Bend, Indiana 46634
- MR Author ID: 267243
- ORCID: 0000-0002-5227-8632
- Email: mkinyon@iusb.edu
- J. D. Phillips
- Affiliation: Department of Mathematics and Computer Science, Wabash College, Crawfordsville, Indiana 47933
- MR Author ID: 322053
- Email: phillipj@wabash.edu
- Received by editor(s): July 8, 2002
- Published electronically: October 3, 2003
- Communicated by: Lance W. Small
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 617-619
- MSC (2000): Primary 20N05
- DOI: https://doi.org/10.1090/S0002-9939-03-07211-3
- MathSciNet review: 2019935