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Santilli Autotopisms of Partial Groups

Received: 8 June 2015     Accepted: 15 June 2015     Published: 11 August 2015
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Abstract

This paper deals with those partial groups that contain a given Santilli isotopism in their autotopism group. A classification of these autotopisms is explicitly determined for partial groups of order n ≤ 4.

Published in American Journal of Modern Physics (Volume 4, Issue 5-1)

This article belongs to the Special Issue Issue I: Foundations of Hadronic Mathematics

DOI 10.11648/j.ajmp.s.2015040501.16
Page(s) 47-51
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Partial Group, Isotopism, Classification

References
[1] A. A. Albert, “Non-associative algebras. I. Fundamental concepts and isotopy,” Ann. of Math. 43:2, pp. 685–707, 1942.
[2] R. H. Bruck, “Some results in the theory of linear non-associative algebras,” Trans. Amer. Math. Soc. 56, pp. 141–199, 1944.
[3] R. M. Santilli, “On a possible Lie-admissible covering of the Galilei Relativity in Newtonian Mechanics for nonconservative and Galilei noninvariant systems,” Hadronic J. 1, pp. 223-423, 1978. Addendum, ibid 1, pp. 1279-1342, 1978.
[4] R. M. Santilli, "Embedding of Lie algebras in Non-Associative Structures,” Nuovo Cimento 51, pp. 570-576, 1967.
[5] R. M. Santilli, ''Lie-admissible invariant representation of irreversibility for matter and antimatter at the classical and operator levels," Nuovo Cimento B 121, pp. 443-486, 2006.
[6] P. Nikolaidou and T. Vougiouklis, “The Lie-Santilli admissible hyperalgebras of type An, “ Ratio Matematica 26, pp. 113-128, 2014.
[7] J. V. Kadeisvili, “An introduction to the Lie-Santilli theory,” Acta Applicandae Mathematicae 50, pp. 131–165, 1998.
[8] R. M. Falcón and J. Núñez, “Fundamentos de la isoteoría de Lie-Santilli,” International Academic Press, America-Europe-Asia, 2001.
[9] R. M. Falcón, J. Núñez and A. Aversa, “Mathematical foundations of Santilli isotopies,” Algebras, Groups and Geometries 32, pp. 135-308, 2015.
[10] R. M. Falcón and J. Núñez, “A particular case of extended isotopisms: Santilli's isotopisms", Hadronic J. 29:3, pp. 285-298, 2006.
[11] R. M. Falcón and J. Núñez, “Partial Latin squares having a Santilli's autotopism in their autotopism groups,” J. Dyn. Syst. Geom. Theor. 5:1, pp. 19-32, 2007.
[12] B. A. Hausmann and O. Ore, “Theory of Quasi-Groups,” Amer. J. Math. 59:4, pp. 983–1004, 1937.
[13] A. A. Albert, “Quasigroups I,” Trans. Am. Math. Soc. 54, pp. 507-519, 1943.
[14] A. A. Albert, “Quasigroups II,” Trans. Am. Math. Soc. 55, pp. 401-419, 1944.
[15] R. H. Bruck, “Some results in the theory of quasigroups,” Trans. Amer. Math. Soc. 55, pp. 19–52, 1944.
[16] B. D. McKay, A. Meynert, and W. Myrvold, “Small Latin squares, quasigroups, and loops,” J. Combin. Des. 15, pp. 98–119, 2007.
[17] A. Hulpke, P. Kaski, and P. R. J. Östergard, “The number of Latin squares of order 11,” Math. Comp. 80, pp. 1197–1219, 2011.
[18] R. M. Falcón, “The set of autotopisms of partial Latin squares”, Discrete Math. 313: 11, pp. 1150–1161, 2013.
[19] R. M. Falcón, “Enumeration and classification of self-orthogonal partial Latin rectangles by using the polynomial method”, European J. Combin. 48, pp. 215–223, 2015.
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  • APA Style

    Raúl M. Falcón, Juan Núñez. (2015). Santilli Autotopisms of Partial Groups. American Journal of Modern Physics, 4(5-1), 47-51. https://doi.org/10.11648/j.ajmp.s.2015040501.16

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    ACS Style

    Raúl M. Falcón; Juan Núñez. Santilli Autotopisms of Partial Groups. Am. J. Mod. Phys. 2015, 4(5-1), 47-51. doi: 10.11648/j.ajmp.s.2015040501.16

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    AMA Style

    Raúl M. Falcón, Juan Núñez. Santilli Autotopisms of Partial Groups. Am J Mod Phys. 2015;4(5-1):47-51. doi: 10.11648/j.ajmp.s.2015040501.16

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  • @article{10.11648/j.ajmp.s.2015040501.16,
      author = {Raúl M. Falcón and Juan Núñez},
      title = {Santilli Autotopisms of Partial Groups},
      journal = {American Journal of Modern Physics},
      volume = {4},
      number = {5-1},
      pages = {47-51},
      doi = {10.11648/j.ajmp.s.2015040501.16},
      url = {https://doi.org/10.11648/j.ajmp.s.2015040501.16},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.s.2015040501.16},
      abstract = {This paper deals with those partial groups that contain a given Santilli isotopism in their autotopism group. A classification of these autotopisms is explicitly determined for partial groups of order n ≤ 4.},
     year = {2015}
    }
    

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    JO  - American Journal of Modern Physics
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Author Information
  • Department of Applied Mathematics I, University of Seville, Seville, Spain

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