On the computations of some homological functors of 2-Engel groups of order at most 16
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 ho...
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| Main Authors: | , , , |
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| Format: | Article |
| Published: |
UKM
2011
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| Subjects: | |
| Online Access: | http://eprints.utm.my/id/eprint/39932/ http://www.ukm.my/jqma/v7_1/jqma-7-1-14-abstractrefs.pdf |
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| Summary: | 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. |
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