Title:
|
Some remarks on simple Bol loops (English) |
Author:
|
Nagy, Gábor P. |
Language:
|
English |
Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
ISSN:
|
0010-2628 (print) |
ISSN:
|
1213-7243 (online) |
Volume:
|
49 |
Issue:
|
2 |
Year:
|
2008 |
Pages:
|
259-270 |
. |
Category:
|
math |
. |
Summary:
|
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. (English) |
Keyword:
|
Bol loop |
Keyword:
|
Bruck loop |
Keyword:
|
simple loop |
MSC:
|
20C20 |
MSC:
|
20F29 |
MSC:
|
20N05 |
idZBL:
|
Zbl 1192.20056 |
idMR:
|
MR2426890 |
. |
Date available:
|
2009-05-05T17:11:08Z |
Last updated:
|
2013-09-22 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119720 |
. |
Reference:
|
[1] Aschbacher M.: On Bol loops of exponent $2$.J. Algebra 288 1 99-136 (2005). Zbl 1090.20037, MR 2138373, 10.1016/j.jalgebra.2005.03.005 |
Reference:
|
[2] Aschbacher M.: Projective planes, loops, and groups.J. Algebra 300 2 396-432 (2006). Zbl 1103.20063, MR 2228204, 10.1016/j.jalgebra.2005.01.058 |
Reference:
|
[3] Aschbacher M., Kinyon M.K., Phillips J.D.: Finite Bruck loops.Trans. Amer. Math. Soc. 358 7 3061-3075 (2005). MR 2216258, 10.1090/S0002-9947-05-03778-5 |
Reference:
|
[4] Baer R.: Nets and groups.Trans. Amer. Math. Soc. 46 110-141 (1939). Zbl 0022.01105, MR 0000035 |
Reference:
|
[5] Bruck R.H.: A Survey of Binary Systems.Springer, Berlin, 1958. Zbl 0141.01401, MR 0093552 |
Reference:
|
[6] Cameron P.J., Korchmáros G.: One-factorizations of complete graphs with a doubly transitive automorphism group.Bull. London Math. Soc. 25 1 (1993), 1-6. MR 1190356, 10.1112/blms/25.1.1 |
Reference:
|
[7] Fischer B.: Distributive Quasigruppen endlicher Ordnung.Math. Z. 83 267-303 (1964). Zbl 0119.26201, MR 0160845, 10.1007/BF01111162 |
Reference:
|
[8] Glauberman G.: On loops of odd order.J. Algebra 1 374-396 (1964). Zbl 0123.01502, MR 0175991, 10.1016/0021-8693(64)90017-1 |
Reference:
|
[9] Grishkov A.N., Zavarnitsine A.V.: Lagrange's theorem for Moufang loops.Math. Proc. Cambridge Philos. Soc. 139 (2005), 1 41-57. Zbl 1091.20039, MR 2155504, 10.1017/S0305004105008388 |
Reference:
|
[10] Hall J.I.: Central automorphisms of Latin square designs and loops.Quasigroups and Related Systems 15 19-46 (2007). MR 2379124 |
Reference:
|
[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. Zbl 0747.22004, MR 1125815 |
Reference:
|
[12] Kiechle H.: Theory of K-loops.Lecture Notes in Mathematics 1778, Springer, Berlin, 2002. Zbl 0997.20059, MR 1899153, 10.1007/b83276 |
Reference:
|
[13] Kiechle H., Kinyon M.K.: Infinite simple Bol loops.Comment. Math. Univ. Carolin. 45 2 275-278 (2004). Zbl 1101.20038, MR 2075275 |
Reference:
|
[14] Kinyon M.K.: LoopForum communication.2007. |
Reference:
|
[15] Liebeck M.W.: The classification of finite simple Moufang loops.Math. Proc. Cambridge Philos. Soc. 102 33-47 (1987). Zbl 0622.20061, MR 0886433, 10.1017/S0305004100067025 |
Reference:
|
[16] Loginov E.K.: Simple Bol loops.Comm. Algebra 35 1 133-144 (2007). Zbl 1136.20054, MR 2287556, 10.1080/00927870601041425 |
Reference:
|
[17] Nagy G.P.: Burnside problems for Moufang and Bol loops of small exponent.Acta Sci. Math. (Szeged) 67 3-4 687-696 (2001). Zbl 0995.20049, MR 1876459 |
Reference:
|
[18] Nagy G.P.: A class of simple proper Bol loops.submitted for publication; download from http://arxiv.org/abs/math.GR/0703919. Zbl 1167.20038, MR 2429915 |
Reference:
|
[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. MR 2515813 |
Reference:
|
[20] Nagy P.T., Strambach K.: Loops in Group Theory and Lie Theory.Walter de Gruyter, Berlin, New York, 2002. Zbl 1050.22001, MR 1899331 |
Reference:
|
[21] Robinson D.A.: Some open questions on Bol loops, mimeographed notes.Oberwolfach Conference on Bol and Moufang Loops, 1976. |
Reference:
|
[22] Thompson J.: Finite groups with fixed-point-free automorphisms of prime order.Proc. Nat. Acad. Sci. U.S.A. 45 578-581 (1959). Zbl 0086.25101, MR 0104731, 10.1073/pnas.45.4.578 |
. |