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Relations between simplicial groups, 3-crossed modules and 2-quadratic modules

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Abstract

In this paper, we define two-quadratic module and explore the relations among twoquadratic modules, three-crossed modules and simplicial groups.

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References

  1. Arvasi, Z., Kuzpınarı, T. S., Uslu, E. Ö.: Three-crossed modules. Homology, Homotopy Appl., 11, 161–187 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  2. Arvasi, Z., Ulualan, E.: On algebraic models for homotopy 3-types. J. Homotopy Relat. Str., 1(1), 1–27 (2006)

    MATH  MathSciNet  Google Scholar 

  3. Baues, H. J.: Combinatorial Homotopy and 4-dimensional Complexes, Walter de Gruyter, 15, 380 pages, 1991

    Book  MATH  Google Scholar 

  4. Baues, H. J., Conduché, D.: The central series for Peiffer commutators in groups with operators. J. Algebra, 133, 1–34 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  5. Carrasco, P.: Complejos Hipercruzados, Cohomologia y Extensiones, Ph.D. Thesis, Univ. de Granada, 1987

    Google Scholar 

  6. Carrasco, P., Cegarra, A. M.: Group-theoretic algebraic models for homotopy types. J. Pure Appl. Algebra, 75, 195–235 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  7. Conduché, D.: Modules croisés généralisés de longueur 2. J. Pure Appl. Algebra, 34, 155–178 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  8. Curtis, E. B.: Simplicial homotopy theory. Adv. in Math., 6, 107–209 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  9. Goerss, P. G., Jardine, J. F.: Simplicial Homotopy Theory, 174, Progres in Mathematics, Birkhäuser, 1999

    Book  MATH  Google Scholar 

  10. Kan, D. M.: A relation between CW-complexes and free c.s.s. groups. Amer. J. Math., 81, 512–528 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  11. May, J. P.: Simplicial Objects in Algebraic Topology, Math. Studies, 11, Van Nostrand, 1967

    Google Scholar 

  12. Mutlu, A., Porter, T.: Applications of Peiffer pairings in the Moore complex of a simplicial group. Theory Appl. Categ., 4, 148–173 (1998)

    MATH  MathSciNet  Google Scholar 

  13. Porter, T.: N-type of simplicial groups and crossed n-cubes. Topology, 32, 5–24 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  14. Whitehead, J. H. C.: Combinatorial homotopy II. Bull. Amer. Math. Soc., 55, 453–496 (1949)

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Hasan Atik.

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Atik, H., Ulualan, E. Relations between simplicial groups, 3-crossed modules and 2-quadratic modules. Acta. Math. Sin.-English Ser. 30, 968–984 (2014). https://doi.org/10.1007/s10114-014-3416-9

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  • DOI: https://doi.org/10.1007/s10114-014-3416-9

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