Computing the nonabelian tensor square of metacyclic p-groups of nilpotency class two
In this paper, we develop appropriate programme using Groups, Algorithms and Programming (GAP) software enables performing different computations on various characteristics of all finite nonabelian metacyclic p–groups, p is prime, of nilpotency class 2. Such programme enables to compute structure of...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Penerbit UTM
2013
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| Online Access: | http://eprints.utm.my/50192/1/NorHanizaSarmin2014_Computingthenonabeliantensor.pdf |
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| author | Sarmin, Nor Haniza Mohd. Ali, Nor Muhainiah Basri, Abdulqader Mohammed Beuerle, James R. |
| author_facet | Sarmin, Nor Haniza Mohd. Ali, Nor Muhainiah Basri, Abdulqader Mohammed Beuerle, James R. |
| author_sort | Sarmin, Nor Haniza |
| collection | ePrints |
| description | In this paper, we develop appropriate programme using Groups, Algorithms and Programming (GAP) software enables performing different computations on various characteristics of all finite nonabelian metacyclic p–groups, p is prime, of nilpotency class 2. Such programme enables to compute structure of the group, order of the group, structure of the center, the number of conjugacy classes, structure of commutator subgroup, abelianization, Whitehead’s universal quadratic functor and other characteristics. In addition, structures of some other groups such as the nonabelian tensor square and various homological functors including Schur multiplier and exterior square can be computed using this programme. Furthermore, by computing the epicenter order or the exterior center order the capability can be determined. In our current article, we only compute the nonabelian tensor square of certain order groups, as an example, and give GAP codes for computing other characteristics and some subgroups |
| first_indexed | 2024-03-05T19:27:41Z |
| format | Article |
| id | utm.eprints-50192 |
| institution | Universiti Teknologi Malaysia - ePrints |
| language | English |
| last_indexed | 2024-03-05T19:27:41Z |
| publishDate | 2013 |
| publisher | Penerbit UTM |
| record_format | dspace |
| spelling | utm.eprints-501922018-09-27T04:12:15Z http://eprints.utm.my/50192/ Computing the nonabelian tensor square of metacyclic p-groups of nilpotency class two Sarmin, Nor Haniza Mohd. Ali, Nor Muhainiah Basri, Abdulqader Mohammed Beuerle, James R. QA Mathematics QA75 Electronic computers. Computer science In this paper, we develop appropriate programme using Groups, Algorithms and Programming (GAP) software enables performing different computations on various characteristics of all finite nonabelian metacyclic p–groups, p is prime, of nilpotency class 2. Such programme enables to compute structure of the group, order of the group, structure of the center, the number of conjugacy classes, structure of commutator subgroup, abelianization, Whitehead’s universal quadratic functor and other characteristics. In addition, structures of some other groups such as the nonabelian tensor square and various homological functors including Schur multiplier and exterior square can be computed using this programme. Furthermore, by computing the epicenter order or the exterior center order the capability can be determined. In our current article, we only compute the nonabelian tensor square of certain order groups, as an example, and give GAP codes for computing other characteristics and some subgroups Penerbit UTM 2013 Article PeerReviewed application/pdf en http://eprints.utm.my/50192/1/NorHanizaSarmin2014_Computingthenonabeliantensor.pdf Sarmin, Nor Haniza and Mohd. Ali, Nor Muhainiah and Basri, Abdulqader Mohammed and Beuerle, James R. (2013) Computing the nonabelian tensor square of metacyclic p-groups of nilpotency class two. Jurnal Teknologi (Sciences and Engineering), 61 (1). pp. 31-34. ISSN 0127-9696 http://dx.doi.org/10.11113/jt.v61.1619 DOI: 10.11113/jt.v61.1619 |
| spellingShingle | QA Mathematics QA75 Electronic computers. Computer science Sarmin, Nor Haniza Mohd. Ali, Nor Muhainiah Basri, Abdulqader Mohammed Beuerle, James R. Computing the nonabelian tensor square of metacyclic p-groups of nilpotency class two |
| title | Computing the nonabelian tensor square of metacyclic p-groups of nilpotency class two |
| title_full | Computing the nonabelian tensor square of metacyclic p-groups of nilpotency class two |
| title_fullStr | Computing the nonabelian tensor square of metacyclic p-groups of nilpotency class two |
| title_full_unstemmed | Computing the nonabelian tensor square of metacyclic p-groups of nilpotency class two |
| title_short | Computing the nonabelian tensor square of metacyclic p-groups of nilpotency class two |
| title_sort | computing the nonabelian tensor square of metacyclic p groups of nilpotency class two |
| topic | QA Mathematics QA75 Electronic computers. Computer science |
| url | http://eprints.utm.my/50192/1/NorHanizaSarmin2014_Computingthenonabeliantensor.pdf |
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