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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:	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
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id	my.utm.39932
record_format	eprints
spelling	my.utm.399322019-03-05T02:54:26Z http://eprints.utm.my/id/eprint/39932/ On the computations of some homological functors of 2-Engel groups of order at most 16 Mat Hassim, Hazzirah Izzati Sarmin, Nor Haniza Mohd. Ali, Nor Muhainiah Mohamad, Mohd. Sham Q Science 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. UKM 2011 Article PeerReviewed 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 http://www.ukm.my/jqma/v7_1/jqma-7-1-14-abstractrefs.pdf
institution	Universiti Teknologi Malaysia
building	UTM Library
collection	Institutional Repository
continent	Asia
country	Malaysia
content_provider	Universiti Teknologi Malaysia
content_source	UTM Institutional Repository
url_provider	http://eprints.utm.my/
topic	Q Science
spellingShingle	Q Science Mat Hassim, Hazzirah Izzati Sarmin, Nor Haniza Mohd. Ali, Nor Muhainiah Mohamad, Mohd. Sham On the computations of some homological functors of 2-Engel groups of order at most 16
description	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.
format	Article
author	Mat Hassim, Hazzirah Izzati Sarmin, Nor Haniza Mohd. Ali, Nor Muhainiah Mohamad, Mohd. Sham
author_facet	Mat Hassim, Hazzirah Izzati Sarmin, Nor Haniza Mohd. Ali, Nor Muhainiah Mohamad, Mohd. Sham
author_sort	Mat Hassim, Hazzirah Izzati
title	On the computations of some homological functors of 2-Engel groups of order at most 16
title_short	On the computations of some homological functors of 2-Engel groups of order at most 16
title_full	On the computations of some homological functors of 2-Engel groups of order at most 16
title_fullStr	On the computations of some homological functors of 2-Engel groups of order at most 16
title_full_unstemmed	On the computations of some homological functors of 2-Engel groups of order at most 16
title_sort	on the computations of some homological functors of 2-engel groups of order at most 16
publisher	UKM
publishDate	2011
url	http://eprints.utm.my/id/eprint/39932/ http://www.ukm.my/jqma/v7_1/jqma-7-1-14-abstractrefs.pdf
_version_	1643650398360174592
score	13.211869

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

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