Commutative subloop-free loops

Martin Beaudry; Louis Marchand

Commentationes Mathematicae Universitatis Carolinae (2011)

  • Volume: 52, Issue: 4, page 473-484
  • ISSN: 0010-2628

Abstract

top
We describe, in a constructive way, a family of commutative loops of odd order, , which have no nontrivial subloops and whose multiplication group is isomorphic to the alternating group .

How to cite

top

Beaudry, Martin, and Marchand, Louis. "Commutative subloop-free loops." Commentationes Mathematicae Universitatis Carolinae 52.4 (2011): 473-484. <http://eudml.org/doc/246242>.

@article{Beaudry2011,
abstract = {We describe, in a constructive way, a family of commutative loops of odd order, $n\ge 7$, which have no nontrivial subloops and whose multiplication group is isomorphic to the alternating group $\mathcal \{A\}_n$.},
author = {Beaudry, Martin, Marchand, Louis},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {loops; multiplication group; alternating group; commutative loops; multiplication groups; alternating groups; partial Latin squares},
language = {eng},
number = {4},
pages = {473-484},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Commutative subloop-free loops},
url = {http://eudml.org/doc/246242},
volume = {52},
year = {2011},
}

TY - JOUR
AU - Beaudry, Martin
AU - Marchand, Louis
TI - Commutative subloop-free loops
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2011
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 52
IS - 4
SP - 473
EP - 484
AB - We describe, in a constructive way, a family of commutative loops of odd order, $n\ge 7$, which have no nontrivial subloops and whose multiplication group is isomorphic to the alternating group $\mathcal {A}_n$.
LA - eng
KW - loops; multiplication group; alternating group; commutative loops; multiplication groups; alternating groups; partial Latin squares
UR - http://eudml.org/doc/246242
ER -

References

top
  1. Albert A.A., 10.1090/S0002-9947-1943-0009962-7, Trans. Amer. Math. Soc. 54 (1943), 507–519. Zbl0063.00039MR0009962DOI10.1090/S0002-9947-1943-0009962-7
  2. Bruck R.H., Contributions to the theory of loops, Trans. Amer. Math. Soc. 60 (1946), 245–354. Zbl0061.02201MR0017288
  3. Bruck R.H., A Survey of Binary Systems, Springer, 1966. Zbl0141.01401MR0093552
  4. Cameron P.J., 10.1016/0012-365X(92)90537-P, Discrete Math 106/107 (1992), 111–115. Zbl0786.20041MR1181904DOI10.1016/0012-365X(92)90537-P
  5. Cavenagh N.J., Greenhill C., Wanless I.M., 10.1002/rsa.20216, Random Structures Algorithms 33 (2008), 286–309. Zbl1202.05015MR2446483DOI10.1002/rsa.20216
  6. Chein O., Pfugfelder H.O., Smith J.D.H., Quasigroups and Loops: Theory and Applications, Helderman, Berlin, 1990. MR1125806
  7. Conway J.H., Hulpke A., McKay J., 10.1112/S1461157000000115, LMS J. Computer Math. 1 (1998), 1–8. Zbl0920.20001MR1635715DOI10.1112/S1461157000000115
  8. Drápal A., Kepka T., 10.1016/S0195-6698(89)80045-9, European J. Combin. 10 (1989), 175–180. Zbl0673.20038MR0988511DOI10.1016/S0195-6698(89)80045-9
  9. Guérin P., Génération des classes d’isomorphisme des boucles d’ordre , Master Thesis, Université du Québec à Chicoutimi, 2003. 
  10. Häggkvist R., Janssen J.C.M., All-even latin squares, Discrete Math. 157 (1996), 199–206. Zbl0864.05017MR1417295
  11. Hall M., 10.1090/S0002-9904-1945-08361-X, Bull. Amer. Math. Soc. 51 (1945), 387–388. Zbl0060.02801MR0013111DOI10.1090/S0002-9904-1945-08361-X
  12. Hall M., The Theory of Groups, Macmillan, New York, 1959. Zbl0919.20001MR0103215
  13. Maenhaut B., Wanless I.M., Webb B.S., 10.1016/j.ejc.2005.07.002, European J. Combin. 28 (2007), 322–336. Zbl1109.05028MR2261822DOI10.1016/j.ejc.2005.07.002
  14. McKay B.D., Meynert A., Myrvold W., 10.1002/jcd.20105, J. Combin. Des. 15 (2007), 98–119. Zbl1112.05018MR2291523DOI10.1002/jcd.20105
  15. Niemenmaa M., Kepka T., 10.1016/0021-8693(90)90152-E, J. Algebra 135 (1990), 112–122. Zbl0706.20046MR1076080DOI10.1016/0021-8693(90)90152-E
  16. Pflugfelder H.O., Quasigroups and Loops: Introduction, Heldermann, Berlin, 1990. Zbl0715.20043MR1125767
  17. Vesanen A., 10.1080/00927879408824900, Comm. Algebra 22 (1994), 1177–1195. MR1261254DOI10.1080/00927879408824900
  18. Wielandt H., Finite Permutation Groups, Academic Press, New York-London, 1964. Zbl0138.02501MR0183775

NotesEmbed ?

top

You must be logged in to post comments.