On the computations of some homological functors of 2-Engel groups of order at most 16

• Main Authors: Mat Hassim, Hazzirah Izzati, Sarmin, Nor Haniza, Mohd. Ali, Nor Muhainiah, Mohamad, Mohd. Sham
• Format: Article
• Published: UKM 2011
• Subjects: Q Science
• Online Access: http://eprints.utm.my/id/eprint/39932/; http://www.ukm.my/jqma/v7_1/jqma-7-1-14-abstractrefs.pdf

The homological functors including J (G) , ∇ (G) , exterior square, the Schur multiplier, Δ (G) , the symmetric square and J (G) of a group were originated in homotopy theory. The nonabelian tensor square which is a special case of the nonabelian tensor product is vital in the computations of the homological functors of a group. It was introduced by Brown and Loday in 1987. The nonabelian tensor square G⊗G of a group G is generated by the symbols g ⊗ h, for all g,h∈G subject to the relations gg′⊗h=(gg′⊗gh)(g⊗h) and g⊗hh′=(g⊗h)(hg⊗hh′), for all g,g′,h,h′ ∈G where g g′ = gg′g−1 . In this paper, the computations of nonabelian tensor squares and some homological functors of all 2-Engel groups of order at most 16 are done. Groups, Algorithms and Programming (GAP) software has been used to assist and verify the results.