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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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 |