The schur multipliers, nonbelian tensor squares and capability of some finite p-groups

The homological functors and nonabelian tensor product have its roots in algebraic K-theory as well as in homotopy theory. Two of the homological functors are the Schur multiplier and nonabelian tensor square, where the nonabelian tensor square is a special case of the nonabelian tensor product. A g...

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Main Author:	Zainal, Rosita
Format:	Thesis
Language:	English
Published:	2016
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/78974/1/RositaZainalPFS2016.pdf
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spelling	my-utm-ep.789742018-09-19T05:21:24Z The schur multipliers, nonbelian tensor squares and capability of some finite p-groups 2016 Zainal, Rosita QA Mathematics The homological functors and nonabelian tensor product have its roots in algebraic K-theory as well as in homotopy theory. Two of the homological functors are the Schur multiplier and nonabelian tensor square, where the nonabelian tensor square is a special case of the nonabelian tensor product. A group is said to be capable if it is a central factor group. In this research, the Schur multiplier, nonabelian tensor square and capability for some groups of order p3, p4, p5 and p6 are determined. An algebraic computation of the center, derived subgroups, abelianization, Schur multipliers, nonabelian tensor squares and capability of the groups are determined with the assistance of Groups, Algorithms and Programming (GAP) software. Using the results of the center, derived subgroups and abelianization, the Schur multiplier, nonabelian tensor square and capability for the groups are determined. The nonabelian tensor squares and capability are also determined using the results of the Schur multipliers. The Schur multiplier of each of the groups considered is found to be trivial or abelian. The results show that the nonabelian tensor square of the groups are always abelian. In addition, a group has been shown to be capable if it has a nontrivial kernel or it is an extra-special p-group with exponent p. 2016 Thesis http://eprints.utm.my/id/eprint/78974/ http://eprints.utm.my/id/eprint/78974/1/RositaZainalPFS2016.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:106252 phd doctoral Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Zainal, Rosita The schur multipliers, nonbelian tensor squares and capability of some finite p-groups
description	The homological functors and nonabelian tensor product have its roots in algebraic K-theory as well as in homotopy theory. Two of the homological functors are the Schur multiplier and nonabelian tensor square, where the nonabelian tensor square is a special case of the nonabelian tensor product. A group is said to be capable if it is a central factor group. In this research, the Schur multiplier, nonabelian tensor square and capability for some groups of order p3, p4, p5 and p6 are determined. An algebraic computation of the center, derived subgroups, abelianization, Schur multipliers, nonabelian tensor squares and capability of the groups are determined with the assistance of Groups, Algorithms and Programming (GAP) software. Using the results of the center, derived subgroups and abelianization, the Schur multiplier, nonabelian tensor square and capability for the groups are determined. The nonabelian tensor squares and capability are also determined using the results of the Schur multipliers. The Schur multiplier of each of the groups considered is found to be trivial or abelian. The results show that the nonabelian tensor square of the groups are always abelian. In addition, a group has been shown to be capable if it has a nontrivial kernel or it is an extra-special p-group with exponent p.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Zainal, Rosita
author_facet	Zainal, Rosita
author_sort	Zainal, Rosita
title	The schur multipliers, nonbelian tensor squares and capability of some finite p-groups
title_short	The schur multipliers, nonbelian tensor squares and capability of some finite p-groups
title_full	The schur multipliers, nonbelian tensor squares and capability of some finite p-groups
title_fullStr	The schur multipliers, nonbelian tensor squares and capability of some finite p-groups
title_full_unstemmed	The schur multipliers, nonbelian tensor squares and capability of some finite p-groups
title_sort	schur multipliers, nonbelian tensor squares and capability of some finite p-groups
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2016
url	http://eprints.utm.my/id/eprint/78974/1/RositaZainalPFS2016.pdf
_version_	1747818117113839616

The schur multipliers, nonbelian tensor squares and capability of some finite p-groups

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