The computation of the nonabelian tensor product of cyclic groups of order p2
Let G and H be groups which act on each other and each of which acts on itself by conjugation, then the actions are compatible if (gh)g' = g(h(g-1 g')) and (hg)h' = h(g(h-1 h')) for g,g'∈G and h,h'∈H. Compatible actions play a very important role in determining the nona...
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| Language: | English |
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Penerbit UTM Press
2012
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| Online Access: | http://eprints.utm.my/47600/1/MohdShamMohamad2012_TheComputationoftheNonabelianTensorProduct.pdf |
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| author | Mohamad, Mohd. Sham Sarmin, Nor Haniza Mohd. Ali, Nor Muhainiah Kappe, Luise Charlotte |
| author_facet | Mohamad, Mohd. Sham Sarmin, Nor Haniza Mohd. Ali, Nor Muhainiah Kappe, Luise Charlotte |
| author_sort | Mohamad, Mohd. Sham |
| collection | ePrints |
| description | Let G and H be groups which act on each other and each of which acts on itself by conjugation, then the actions are compatible if (gh)g' = g(h(g-1 g')) and (hg)h' = h(g(h-1 h')) for g,g'∈G and h,h'∈H. Compatible actions play a very important role in determining the nonabelian tensor product. The nonabelian tensor product, G⊗H, was introduced by Brown and Loday in 1984. The nonabelian tensor product is the group generated by g⊗h with two relations gg'⊗h = (gg'⊗gh)(g⊗h) and g⊗hh' = (g⊗h)(hg⊗hh') for g,g'∈G and h,h'∈H, where G and H act on each other in a compatible fashion and act on themselves by conjugation. In 1987, Brown et al. gave an open problem in determining whether the tensor product of two cyclic groups is cyclic. Visscher in 1998 has shown that the nonabelian tensor product is not necessarily cyclic, but he only focused on the case of cyclic groups of 2-power order where the action is of order two. In this paper, the compatibility and the nonabelian tensor product of cyclic groups of order p2 with the actions of order p are determined. |
| first_indexed | 2024-03-05T19:23:15Z |
| format | Article |
| id | utm.eprints-47600 |
| institution | Universiti Teknologi Malaysia - ePrints |
| language | English |
| last_indexed | 2024-03-05T19:23:15Z |
| publishDate | 2012 |
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| spelling | utm.eprints-476002020-02-27T03:05:00Z http://eprints.utm.my/47600/ The computation of the nonabelian tensor product of cyclic groups of order p2 Mohamad, Mohd. Sham Sarmin, Nor Haniza Mohd. Ali, Nor Muhainiah Kappe, Luise Charlotte TK Electrical engineering. Electronics Nuclear engineering Let G and H be groups which act on each other and each of which acts on itself by conjugation, then the actions are compatible if (gh)g' = g(h(g-1 g')) and (hg)h' = h(g(h-1 h')) for g,g'∈G and h,h'∈H. Compatible actions play a very important role in determining the nonabelian tensor product. The nonabelian tensor product, G⊗H, was introduced by Brown and Loday in 1984. The nonabelian tensor product is the group generated by g⊗h with two relations gg'⊗h = (gg'⊗gh)(g⊗h) and g⊗hh' = (g⊗h)(hg⊗hh') for g,g'∈G and h,h'∈H, where G and H act on each other in a compatible fashion and act on themselves by conjugation. In 1987, Brown et al. gave an open problem in determining whether the tensor product of two cyclic groups is cyclic. Visscher in 1998 has shown that the nonabelian tensor product is not necessarily cyclic, but he only focused on the case of cyclic groups of 2-power order where the action is of order two. In this paper, the compatibility and the nonabelian tensor product of cyclic groups of order p2 with the actions of order p are determined. Penerbit UTM Press 2012 Article PeerReviewed application/pdf en http://eprints.utm.my/47600/1/MohdShamMohamad2012_TheComputationoftheNonabelianTensorProduct.pdf Mohamad, Mohd. Sham and Sarmin, Nor Haniza and Mohd. Ali, Nor Muhainiah and Kappe, Luise Charlotte (2012) The computation of the nonabelian tensor product of cyclic groups of order p2. Jurnal Teknologi (Sciences and Engineering), 57 (SUP. 1). pp. 35-44. ISSN 0127-9696 https://dx.doi.org/10.11113/jt.v57.1521 DOI:10.11113/jt.v57.1521 |
| spellingShingle | TK Electrical engineering. Electronics Nuclear engineering Mohamad, Mohd. Sham Sarmin, Nor Haniza Mohd. Ali, Nor Muhainiah Kappe, Luise Charlotte The computation of the nonabelian tensor product of cyclic groups of order p2 |
| title | The computation of the nonabelian tensor product of cyclic groups of order p2 |
| title_full | The computation of the nonabelian tensor product of cyclic groups of order p2 |
| title_fullStr | The computation of the nonabelian tensor product of cyclic groups of order p2 |
| title_full_unstemmed | The computation of the nonabelian tensor product of cyclic groups of order p2 |
| title_short | The computation of the nonabelian tensor product of cyclic groups of order p2 |
| title_sort | computation of the nonabelian tensor product of cyclic groups of order p2 |
| topic | TK Electrical engineering. Electronics Nuclear engineering |
| url | http://eprints.utm.my/47600/1/MohdShamMohamad2012_TheComputationoftheNonabelianTensorProduct.pdf |
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