Some remarks on simple Bol loops

Gábor P. Nagy

Commentationes Mathematicae Universitatis Carolinae (2008)

  • Volume: 49, Issue: 2, page 259-270
  • ISSN: 0010-2628

Abstract

top
In this paper we make some remarks on simple Bol loops which were motivated by questions at the LOOPS'07 conference. We also list some open problems on simple loops.

How to cite

top

Nagy, Gábor P.. "Some remarks on simple Bol loops." Commentationes Mathematicae Universitatis Carolinae 49.2 (2008): 259-270. <http://eudml.org/doc/250485>.

@article{Nagy2008,
abstract = {In this paper we make some remarks on simple Bol loops which were motivated by questions at the LOOPS'07 conference. We also list some open problems on simple loops.},
author = {Nagy, Gábor P.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Bol loop; Bruck loop; simple loop; Bol loops; Bruck loops; simple loops},
language = {eng},
number = {2},
pages = {259-270},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Some remarks on simple Bol loops},
url = {http://eudml.org/doc/250485},
volume = {49},
year = {2008},
}

TY - JOUR
AU - Nagy, Gábor P.
TI - Some remarks on simple Bol loops
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2008
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 49
IS - 2
SP - 259
EP - 270
AB - In this paper we make some remarks on simple Bol loops which were motivated by questions at the LOOPS'07 conference. We also list some open problems on simple loops.
LA - eng
KW - Bol loop; Bruck loop; simple loop; Bol loops; Bruck loops; simple loops
UR - http://eudml.org/doc/250485
ER -

References

top
  1. Aschbacher M., 10.1016/j.jalgebra.2005.03.005, J. Algebra 288 1 99-136 (2005). (2005) Zbl1090.20037MR2138373DOI10.1016/j.jalgebra.2005.03.005
  2. Aschbacher M., 10.1016/j.jalgebra.2005.01.058, J. Algebra 300 2 396-432 (2006). (2006) Zbl1103.20063MR2228204DOI10.1016/j.jalgebra.2005.01.058
  3. Aschbacher M., Kinyon M.K., Phillips J.D., 10.1090/S0002-9947-05-03778-5, Trans. Amer. Math. Soc. 358 7 3061-3075 (2005). (2005) MR2216258DOI10.1090/S0002-9947-05-03778-5
  4. Baer R., Nets and groups, Trans. Amer. Math. Soc. 46 110-141 (1939). (1939) Zbl0022.01105MR0000035
  5. Bruck R.H., A Survey of Binary Systems, Springer, Berlin, 1958. Zbl0141.01401MR0093552
  6. Cameron P.J., Korchmáros G., 10.1112/blms/25.1.1, Bull. London Math. Soc. 25 1 (1993), 1-6. (1993) MR1190356DOI10.1112/blms/25.1.1
  7. Fischer B., 10.1007/BF01111162, Math. Z. 83 267-303 (1964). (1964) Zbl0119.26201MR0160845DOI10.1007/BF01111162
  8. Glauberman G., 10.1016/0021-8693(64)90017-1, J. Algebra 1 374-396 (1964). (1964) Zbl0123.01502MR0175991DOI10.1016/0021-8693(64)90017-1
  9. Grishkov A.N., Zavarnitsine A.V., 10.1017/S0305004105008388, Math. Proc. Cambridge Philos. Soc. 139 (2005), 1 41-57. (2005) Zbl1091.20039MR2155504DOI10.1017/S0305004105008388
  10. Hall J.I., Central automorphisms of Latin square designs and loops, Quasigroups and Related Systems 15 19-46 (2007). (2007) MR2379124
  11. Hofmann K.H., Strambach K., Topological and analytic loops, Quasigroups and Loops: Theory and Applications, pp.205-262, Sigma Ser. Pure Math. 8, Heldermann, Berlin, 1990. Zbl0747.22004MR1125815
  12. Kiechle H., 10.1007/b83276, Lecture Notes in Mathematics 1778, Springer, Berlin, 2002. Zbl0997.20059MR1899153DOI10.1007/b83276
  13. Kiechle H., Kinyon M.K., Infinite simple Bol loops, Comment. Math. Univ. Carolin. 45 2 275-278 (2004). (2004) Zbl1101.20038MR2075275
  14. Kinyon M.K., LoopForum communication, 2007. 
  15. Liebeck M.W., 10.1017/S0305004100067025, Math. Proc. Cambridge Philos. Soc. 102 33-47 (1987). (1987) Zbl0622.20061MR0886433DOI10.1017/S0305004100067025
  16. Loginov E.K., 10.1080/00927870601041425, Comm. Algebra 35 1 133-144 (2007). (2007) Zbl1136.20054MR2287556DOI10.1080/00927870601041425
  17. Nagy G.P., Burnside problems for Moufang and Bol loops of small exponent, Acta Sci. Math. (Szeged) 67 3-4 687-696 (2001). (2001) Zbl0995.20049MR1876459
  18. Nagy G.P., A class of simple proper Bol loops, submitted for publication; download from http://arxiv.org/abs/math.GR/0703919. Zbl1167.20038MR2429915
  19. Nagy G.P., A class of finite simple Bol loops of exponent 2 , Trans. Am. Math. Soc., to appear; download from http://arxiv.org/abs/0709.4544v1. MR2515813
  20. Nagy P.T., Strambach K., Loops in Group Theory and Lie Theory, Walter de Gruyter, Berlin, New York, 2002. Zbl1050.22001MR1899331
  21. Robinson D.A., Some open questions on Bol loops, mimeographed notes, Oberwolfach Conference on Bol and Moufang Loops, 1976. 
  22. Thompson J., 10.1073/pnas.45.4.578, Proc. Nat. Acad. Sci. U.S.A. 45 578-581 (1959). (1959) Zbl0086.25101MR0104731DOI10.1073/pnas.45.4.578

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.