| Title:
|
Bol-loops of order $3\cdot 2^n$ (English) |
| Author:
|
Wagner, Daniel |
| Author:
|
Wopperer, Stefan |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
46 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
85-88 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this article we construct proper Bol-loops of order $3\cdot 2^n$ using a generalisation of the semidirect product of groups defined by Birkenmeier and Xiao. Moreover we classify the obtained loops up to isomorphism. (English) |
| Keyword:
|
bol-loop |
| Keyword:
|
loop |
| Keyword:
|
group |
| Keyword:
|
semidirect product |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1143.20046 |
| idMR:
|
MR2387496 |
| . |
| Date available:
|
2009-08-27T10:12:18Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133390 |
| . |
| Reference:
|
[1] Kiguradze I. T.: On Some Singular Boundary Value Problems for Ordinary Differential Equations. : Tbilisi Univ. Press, Tbilisi., 1975 (in Russian). MR 0499402 |
| Reference:
|
[2] Kiguradze I. T., Shekhter B. L.: Singular boundary value problems for second order ordinary differential equations.Itogi Nauki i Tekhniki Ser. Sovrem. Probl. Mat. Nov. Dost. 30 (1987), 105–201 (in Russian), translated in J. Soviet Math. 43 (1988), 2340–2417. Zbl 0631.34021, MR 0925830 |
| Reference:
|
[3] O’Regan D.: Upper and lower solutions for singular problems arising in the theory of membrane response of a spherical cap.Nonlinear Anal. 47 (2001), 1163–1174. Zbl 1042.34523, MR 1970727 |
| Reference:
|
[4] O’Regan D.: Theory of Singular Boundary Value Problems. : World Scientific, Singapore., 1994. MR 1286741 |
| Reference:
|
[5] Rachůnková I.: Singular mixed boundary value problem.J. Math. Anal. Appl. 320 (2006), 611–618. Zbl 1103.34009, MR 2225980 |
| Reference:
|
[6] Rachůnková I., Staněk S., Tvrdý M.: Singularities and Laplacians in Boundary Value Problems for Nonlinear Ordinary Differential Equations.Handbook of Differential Equations. Ordinary Differential Equations, Ed. by A. Cañada, P. Drábek, A. Fonda, Vol. 3., pp. 607–723, Elsevier, 2006. |
| Reference:
|
[7] Wang M., Cabada A., Nieto J. J.: Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions.Ann. Polon. Math. 58, 3 (1993), 221–235. Zbl 0789.34027, MR 1244394 |
| . |
