Bol-loops of order 3 · 2 n

Daniel Wagner; Stefan Wopperer

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2007)

  • Volume: 46, Issue: 1, page 85-88
  • ISSN: 0231-9721

Abstract

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In this article we construct proper Bol-loops of order 3 · 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.

How to cite

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Wagner, Daniel, and Wopperer, Stefan. "Bol-loops of order $3\cdot 2^n$." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 46.1 (2007): 85-88. <http://eudml.org/doc/32458>.

@article{Wagner2007,
abstract = {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.},
author = {Wagner, Daniel, Wopperer, Stefan},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {bol-loop; loop; group; semidirect product; Bol loops; semidirect products of groups},
language = {eng},
number = {1},
pages = {85-88},
publisher = {Palacký University Olomouc},
title = {Bol-loops of order $3\cdot 2^n$},
url = {http://eudml.org/doc/32458},
volume = {46},
year = {2007},
}

TY - JOUR
AU - Wagner, Daniel
AU - Wopperer, Stefan
TI - Bol-loops of order $3\cdot 2^n$
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2007
PB - Palacký University Olomouc
VL - 46
IS - 1
SP - 85
EP - 88
AB - 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.
LA - eng
KW - bol-loop; loop; group; semidirect product; Bol loops; semidirect products of groups
UR - http://eudml.org/doc/32458
ER -

References

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  1. Kiguradze I. T.: On Some Singular Boundary Value Problems for Ordinary Differential Equations., Tbilisi Univ. Press, Tbilisi, , 1975 (in Russian). (1975) MR0499402
  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. (1987) Zbl0631.34021MR0925830
  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. Zbl1042.34523MR1970727
  4. O’Regan D.: Theory of Singular Boundary Value Problems., World Scientific, Singapore, , 1994. (1994) MR1286741
  5. Rachůnková I., Singular mixed boundary value problem, J. Math. Anal. Appl. 320 (2006), 611–618. Zbl1103.34009MR2225980
  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. 
  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. (1993) Zbl0789.34027MR1244394

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