Moufang loops of order 243

Michael C. Slattery; Ashley L. Zenisek

Commentationes Mathematicae Universitatis Carolinae (2012)

  • Volume: 53, Issue: 3, page 423-428
  • ISSN: 0010-2628

Abstract

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We present a computer-assisted determination of the 72 non-isomorphic, non-associative Moufang loops of order 243. Some of their properties and distinguishing features are discussed.

How to cite

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Slattery, Michael C., and Zenisek, Ashley L.. "Moufang loops of order 243." Commentationes Mathematicae Universitatis Carolinae 53.3 (2012): 423-428. <http://eudml.org/doc/246733>.

@article{Slattery2012,
abstract = {We present a computer-assisted determination of the 72 non-isomorphic, non-associative Moufang loops of order 243. Some of their properties and distinguishing features are discussed.},
author = {Slattery, Michael C., Zenisek, Ashley L.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Moufang; finite loops; classification of Moufang loops; GAP; finite loops; classification of Moufang loops; Moufang loops of order 243; nonassociative Moufang loops; GAP; central extensions},
language = {eng},
number = {3},
pages = {423-428},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Moufang loops of order 243},
url = {http://eudml.org/doc/246733},
volume = {53},
year = {2012},
}

TY - JOUR
AU - Slattery, Michael C.
AU - Zenisek, Ashley L.
TI - Moufang loops of order 243
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2012
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 53
IS - 3
SP - 423
EP - 428
AB - We present a computer-assisted determination of the 72 non-isomorphic, non-associative Moufang loops of order 243. Some of their properties and distinguishing features are discussed.
LA - eng
KW - Moufang; finite loops; classification of Moufang loops; GAP; finite loops; classification of Moufang loops; Moufang loops of order 243; nonassociative Moufang loops; GAP; central extensions
UR - http://eudml.org/doc/246733
ER -

References

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  1. Chee W.L., Classification of Moufang loops of odd order, PhD thesis, Universiti Sains Malaysia, 2010. 
  2. Chein O., 10.1090/S0002-9947-1974-0330336-3, Trans. Amer. Math. Soc. 188 (1974), 31–51. MR0330336DOI10.1090/S0002-9947-1974-0330336-3
  3. Chein O., Pflugfelder H.O., 10.1007/BF01222620, Arch. Math. (Basel) 22 (1971), 573–576. Zbl0241.20061MR0297914DOI10.1007/BF01222620
  4. Chein O., Pflugfelder H.O., Moufang loops of small order, Mem. Amer. Math. Soc. 13 (1978), 1–131. MR0466391
  5. The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4 . 4 . 12 , (2008), . 
  6. Nagy G., Valsecchi M., 10.1016/j.jalgebra.2006.01.031, J. Algebra 307 (2007), 547–564. Zbl1117.20050MR2275362DOI10.1016/j.jalgebra.2006.01.031
  7. Nagy G., Vojtěchovský P., LOOPS: Computing with quasigroups and loops in GAP, Version 2 . 0 . 0 , (2008), . 
  8. Nagy G., Vojtěchovský P., 10.1016/j.jsc.2007.06.004, J. Symbolic Comput. 42 (2007), 871–883. Zbl1131.20053MR2355056DOI10.1016/j.jsc.2007.06.004

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