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Original Articles

Extension of Maschke’s theorem

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Pages 2192-2203 | Received 11 Jul 2018, Accepted 22 Sep 2018, Published online: 22 Feb 2019

References

  • Burn, R. P. (1978). Finite Bol loops. Math. Proc. Camb. Phil. Soc. 84(3): 377–386.
  • Drazin, M. P. (1981). Maschke’s theorem for semigroups. J. Algebra 72(1):269–278.
  • Foguel, T., Ungar, A. A. (2001). Gyrogroups and the decomposition of groups into twisted subgroups and subgroups. Pacific J. Math. 197(1):1–11.
  • Gerstenhaber, M., Schaps, M. E. (1996). The modular version of Maschke’s theorem for normal abelian p-Sylows. J. Pure Appl. Algebra 108(3):257–264.
  • Kiechle, H. (2002). Theory of K-Loops, Lecture Notes in Mathematics, Vol.1778. Berlin: Springer-Verlag.
  • Passman, D. S. (1983). It’s essentially Maschke’s theorem. Rocky Mountain J. Math. 13(1):37–54.
  • Roman, S. (2008). Advanced Linear Algebra. Graduate Texts in Mathematics, Vol. 135, 3rd ed. New York: Springer-Verlag.
  • Suksumran, T. (2016). The algebra of gyrogroups: Cayley’s Theorem, Lagrange’s Theorem, and Isomorphism Theorems. In: Rassias, Th. M. and Pardalos, P. M., eds. Essays in Mathematics and Its Applications: In Honor of Vladimir Arnold. Basel, Switzerland: Springer, pp. 369–437.
  • Suksumran, T. (2016). Gyrogroup actions: A generalization of group actions. J. Algebra 454:70–91.
  • Suksumran, T., Wiboonton, K. (2014). Lagrange’s theorem for gyrogroups and the Cauchy property. Quasigroups Relat. Syst. 22(2):283–294.
  • Suksumran, T., Wiboonton, K. (2017). Möbius’s functional equation and Schur’s lemma with applications to the complex unit disk. Aequat. Math. 91(3):491–503.
  • Ungar, A. A. (2007). Einstein’s velocity addition law and its hyperbolic geometry. Comput. Math. Appl. 53(8):1228–1250.
  • Ungar, A. A. (2008). Analytic Hyperbolic Geometry and Albert Einstein’s Special Theory of Relativity. Hackensack, NJ: World Scientific.
  • Ungar, A. A. (2008). From Möbius to gyrogroups. Amer. Math. Monthly 115(2):138–144.
  • Zhai, W., Zhang, L. (2011). Maschke’s theorem for smash products of quasitriangular weak Hopf algebras. Abh. Math. Semin. Univ. Hambg. 81(1):35–44.

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