Capability and homological functors of infinite two - generator groups of nilpotency class two

A group is called capable if it is a central factor group. Baer characterized finitely generated abelian groups which are capable as those groups which have two or more factors of maximal order in their direct decomposition. The capability of groups have been determined for infinite metacyclic group...

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Main Author:	Mohd. Ali, Nor Muhainiah
Format:	Thesis
Language:	English
Published:	2009
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/13579/1/NorMuhainiahAliPFS2009.pdf
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id	my-utm-ep.13579
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spelling	my-utm-ep.135792018-06-25T08:59:50Z Capability and homological functors of infinite two - generator groups of nilpotency class two 2009 Mohd. Ali, Nor Muhainiah QA Mathematics A group is called capable if it is a central factor group. Baer characterized finitely generated abelian groups which are capable as those groups which have two or more factors of maximal order in their direct decomposition. The capability of groups have been determined for infinite metacyclic groups and for 2-generator p-group of nilpotency class two (p prime). The remaining case for capability of 2-generator group of nilpotency class two is the infinite case where the groups have been classified by Sarmin in 2002. Let R be the class of infinite 2-generator groups of nilpotency class two. Using their classification and non-abelian tensor squares, the capability of groups in R are determined. Brown and Loday in 1984 and 1987 introduced the nonabelian tensor square of a group to be a special case of the nonabelian tensor product which has its origin in algebraic K-theory as well as in homotopy theory. The homological functors have been determined for infinite metacyclic groups and non-abelian 2-generator p-groups of nilpotency class two. Therefore, the homological functors including the exterior square, the symmetric square and the Schur multiplier of groups in R will also be determined in this research. 2009 Thesis http://eprints.utm.my/id/eprint/13579/ http://eprints.utm.my/id/eprint/13579/1/NorMuhainiahAliPFS2009.pdf application/pdf en public 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 Mohd. Ali, Nor Muhainiah Capability and homological functors of infinite two - generator groups of nilpotency class two
description	A group is called capable if it is a central factor group. Baer characterized finitely generated abelian groups which are capable as those groups which have two or more factors of maximal order in their direct decomposition. The capability of groups have been determined for infinite metacyclic groups and for 2-generator p-group of nilpotency class two (p prime). The remaining case for capability of 2-generator group of nilpotency class two is the infinite case where the groups have been classified by Sarmin in 2002. Let R be the class of infinite 2-generator groups of nilpotency class two. Using their classification and non-abelian tensor squares, the capability of groups in R are determined. Brown and Loday in 1984 and 1987 introduced the nonabelian tensor square of a group to be a special case of the nonabelian tensor product which has its origin in algebraic K-theory as well as in homotopy theory. The homological functors have been determined for infinite metacyclic groups and non-abelian 2-generator p-groups of nilpotency class two. Therefore, the homological functors including the exterior square, the symmetric square and the Schur multiplier of groups in R will also be determined in this research.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Mohd. Ali, Nor Muhainiah
author_facet	Mohd. Ali, Nor Muhainiah
author_sort	Mohd. Ali, Nor Muhainiah
title	Capability and homological functors of infinite two - generator groups of nilpotency class two
title_short	Capability and homological functors of infinite two - generator groups of nilpotency class two
title_full	Capability and homological functors of infinite two - generator groups of nilpotency class two
title_fullStr	Capability and homological functors of infinite two - generator groups of nilpotency class two
title_full_unstemmed	Capability and homological functors of infinite two - generator groups of nilpotency class two
title_sort	capability and homological functors of infinite two - generator groups of nilpotency class two
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2009
url	http://eprints.utm.my/id/eprint/13579/1/NorMuhainiahAliPFS2009.pdf
_version_	1747814961978015744

Capability and homological functors of infinite two - generator groups of nilpotency class two

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