The Nonabelian Tensor Squares and Homological Functors of Some 2-Engel Groups

  • Hazzirah Izzati Mat Hassim
  • Nor Haniza Sarmin
  • Nor Muhainiah Mohd Ali
Keywords: nonabelian tensor square, homological functors, 2-Engel group

Abstract

Originated in homotopy theory, the nonabelian tensor square is a special case of the nonabelian tensor product. The nonabelian tensor square of a group G, denoted as G7G is generated by the symbols g7h, for all g, hdG subject to the relations gg'7h = (gg'7gh) (g7h) and g7hh' = (g7h)(hg7hh'), for all g, g', h, h'dG where the action is taken to be conjugation. The homological functors of a group including J(G), d(G), the exterior square, the Schur multiplier, d(G), the symmetric square and J (G) d(G) are closely related to the nonabelian tensor square of the group. In this paper, the nonabelian tensor squares and homological functors of some 2-Engel groups will be presented.

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Author Biographies

Hazzirah Izzati Mat Hassim

Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor

Nor Haniza Sarmin

Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor

Nor Muhainiah Mohd Ali

Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor

Published
2019-01-19
How to Cite
Mat Hassim, H. I., Sarmin, N. H., & Mohd Ali, N. M. (2019). The Nonabelian Tensor Squares and Homological Functors of Some 2-Engel Groups. Journal of Science and Mathematics Letters, 4(1), 53-59. Retrieved from https://ejournal.upsi.edu.my/index.php/JSML/article/view/361