Generalization of the Central Subgroup of the Nonabelian Tensor Square of a Crystallographic Group with Symmetric Point Group

Rohaidah Masri, Tan Yee Ting, Nor'ashiqin Mohd. Idrus

Abstract


The central subgroup of the nonabelian tensor square of a group  denoted by is a crucial tool in exploring the properties of a group. It is a normal subgroup generated by the element  for all  In this paper, the central subgroup of the nonabelian tensor square of a crystallographic group with symmetric point group is constructed and generalized up to finite dimension. 


Keywords


Central subgroup of the nonabelian tensor square; Crystallographic group

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References


Y. T. Tan, N. Mohd. Idrus, R. Masri, W. N. F. Wan Mohd Fauzi, N. H. Sarmin and H. I. Mat Hassim, On the abelianization all Bieberbach groups of dimension four with symmetric point group of order six, AIP Conference Proceedings 1635 (2014), 479-486.

R. Brown and J. L. Loday, Van kampen theorems for diagrams of spaces, Topology 26 (1987), 311-335.

R. D. Blyth, F. Fumagalli and M. Morigi, Some structural results on the non-abelian tensor square of groups, Journal of Group Theory 13 (2010), 83-94.

Y. T. Tan, N. Mohd. Idrus, R. Masri, W. N. F. Wan Mohd Fauzi and N. H. Sarmin, The central subgroup of the nonabelian tensors square of all Bieberbach groups of dimension four with symmetric point group of order six, 2nd International Postgraduate Conference on Science and Mathematics 2014.

B. Eick and W. Nickel, Computing Schur multiplicator and tensor square of polycyclic group, Journal of Algebra 320(2) (2008), 927-944.

N. R. Rocco, On a construction related to the nonabelian tensor square of a group, Bol. Soc. Brasil. Mat. (N. S.) 22 (1991), 63-79.

R. Masri, The nonabelian tensor squares of certain Bieberbach groups with cyclic point groups, Ph.D. Thesis, Universiti Teknologi Malaysia (2009).




DOI: http://dx.doi.org/10.26713%2Fjims.v8i4.556

eISSN 0975-5748; pISSN 0974-875X