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
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Online Access:http://eprints.utm.my/id/eprint/13579/1/NorMuhainiahAliPFS2009.pdf
http://eprints.utm.my/id/eprint/13579/
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Institution: Universiti Teknologi Malaysia
Language: English
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spelling my.utm.135792018-06-25T08:59:50Z http://eprints.utm.my/id/eprint/13579/ Capability and homological functors of infinite two - generator groups of nilpotency class two 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 NonPeerReviewed application/pdf en http://eprints.utm.my/id/eprint/13579/1/NorMuhainiahAliPFS2009.pdf Mohd. Ali, Nor Muhainiah (2009) Capability and homological functors of infinite two - generator groups of nilpotency class two. PhD thesis, Universiti Teknologi Malaysia, Faculty of Science.
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/
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
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
publishDate 2009
url http://eprints.utm.my/id/eprint/13579/1/NorMuhainiahAliPFS2009.pdf
http://eprints.utm.my/id/eprint/13579/
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