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 |
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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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