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

Mat Hassim, Hazzirah Izzati and Sarmin, Nor Haniza and Mohd. Ali, Nor Muhainiah and Mohamad, Mohd. Sham (2011) On the computations of some homological functors of 2-Engel groups of order at most 16. Journal of Quality Measurement and Analysis, 7 (1). pp. 153-159. ISSN 1823-5670

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Official URL: http://www.ukm.my/jqma/v7_1/jqma-7-1-14-abstractre...

Abstract

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.

Item Type:Article
Uncontrolled Keywords:Nonabelian tensor square, homological functors, 2-Engel groups, GAP
Subjects:Q Science
Divisions:Science
ID Code:39932
Deposited By: Fazli Masari
Deposited On:21 Jul 2014 13:20
Last Modified:05 Mar 2019 10:54

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