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SOME ALGEBRAIC AND TOPOLOGICAL PROPERTIES OF THE NONABELIAN TENSOR PRODUCT

  • Otera, Daniele Ettore (Departement de Mathematique Universite Paris Sud 11) ;
  • Russo, Francesco G. (DEIM Universita degli Studi di Palermo, Department of Mathematics Universiti Teknologi Malaysia) ;
  • Tanasi, Corrado (Dipartimento di Matematica e Informatica Universita degli Studi di Palermo)
  • Received : 2012.01.17
  • Published : 2013.07.31

Abstract

Several authors investigated the properties which are invariant under the passage from a group to its nonabelian tensor square. In the present note we study this problem from the viewpoint of the classes of groups and the methods allow us to prove a result of invariance for some geometric properties of discrete groups.

Keywords

References

  1. W. A. Bogley and N. D. Gilbert, The homology of Peiffer products of groups, New York J. Math. 6 (2000), 55-71.
  2. S. G. Brick and M. L. Mihalik, The QSF property for groups and spaces, Math. Z. 220 (1995), no. 2, 207-217. https://doi.org/10.1007/BF02572610
  3. S. G. Brick and M. L. Mihalik, Group extensions are quasi-simply-filtrated, Bull. Austral.Math. Soc. 50 (1994), no. 1, 21-27. https://doi.org/10.1017/S0004972700009527
  4. R. Brown, D. L. Johnson, and E. F. Robertson, Some computations of nonabelian tensor products of groups, J. Algebra 111 (1987), no. 1, 177-202. https://doi.org/10.1016/0021-8693(87)90248-1
  5. R. Brown and J.-L. Loday, Van Kampen theorems for diagrams of spaces, Topology 26 (1987), no. 3, 311-335. https://doi.org/10.1016/0040-9383(87)90004-8
  6. A. Erfanian, F. G. Russo, and N. H. Sarmin, Some considerations on the nonabelian tensor square of crystallographic groups, Asian-Eur. J. Math. 4 (2011), no. 2, 271-282. https://doi.org/10.1142/S1793557111000216
  7. A. Erfanian, N. M. Mohd Ali, S. Rashid, and N. H. Sarmin, On the nonabelian tensor square and capability of groups of order $p2q$, Arch. Math. (Basel) 97 (2011), no. 4, 299-306. https://doi.org/10.1007/s00013-011-0304-8
  8. L. Funar and D. E. Otera, On the wgsc and qsf tameness conditions for finitely presented groups, Groups Geom. Dyn. 4 (2010), no. 3, 549-596.
  9. N. Gilbert and P. Higgins, The nonabelian tensor product of groups and related constructions, Glasgow Math. J. 31 (1989), no. 1, 17-29. https://doi.org/10.1017/S0017089500007515
  10. T. Hannebauer, On non-abelian tensor squares of linear groups, Arch. Math. (Basel) 55 (1990), no. 1, 30-34. https://doi.org/10.1007/BF01199111
  11. N. Inassaridze, Nonabelian tensor products and nonabelian homology of groups, J. Pure Appl. Algebra 112 (1996), no. 2, 191-205. https://doi.org/10.1016/0022-4049(95)00133-6
  12. I. Nakaoka, Non-abelian tensor products of solvable groups, J. Group Theory 3 (2000), no. 2, 157-167.
  13. D. E. Otera and F. G. Russo, On the WGSC property in some classes of groups, Mediterr. J. Math. 6 (2009), no. 4, 501-508. https://doi.org/10.1007/s00009-009-0021-8
  14. D. J. Robinson, A Course in the Theory of Groups, Springer, Berlin, 1982.
  15. N. R. Rocco, On a construction related to the nonabelian tensor square of a group, Bol. Soc. Brasil. Mat. (N.S.) 22 (1991), no. 1, 63-79. https://doi.org/10.1007/BF01244898
  16. F. G. Russo, Nonabelian tensor product of soluble minimax groups, Proceedings of Computational Group Theory and Cohomology (Harlaxton, 2008), 179-182, Contemporary Mathematics, American Mathematical Society, New York. 2010.
  17. F. G. Russo, A generalization of groups with many almost normal subgroups, Algebra Discrete Math. 9 (2010), no. 1, 79-85.
  18. J. R. Stallings, Brick's quasi-simple filtrations for groups and 3-manifolds, Procedings of Geometric Group Theory, Vol. 1 (Sussex, 1991), 188-203, London Math. Soc. Lecture Note Ser. 181, Cambridge University Press, Cambridge. 1993.
  19. V. Z. Thomas, The non-abelian tensor product of finite groups is finite: a homology-free proof, Glasg. Math. J. 52 (2010), no. 3, 473-477. https://doi.org/10.1017/S0017089510000352
  20. M. P. Visscher, On the nilpotency class and solvability length of nonabelian tensor product of groups, Arch. Math. (Basel) 73 (1999), no. 3, 161-171. https://doi.org/10.1007/PL00000400

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