The third natural representation of the symmetric groups
DOI:
https://doi.org/10.5269/bspm.78612Abstract
The intension of this work is to analyze the third natural representation module, M3(n)=KSnx1x2x3 and we concentrate our work on finding exact sequence for the KSn-submodules.
References
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2. H. K. Farahat, On the natural representation of the symmetric groups, Proc. Glasgow Math. Assoc., vol. 5, part 3, 1962, 121–136.
3. M. Al-Jilihawi, On the natural representations of the symmetric groups, M.Sc. Thesis, College of Education - Almustansirya University, 1996.
4. M. H. Peel, On the second natural representation of the symmetric groups, Proc. Glasgow Math. Assoc., vol. 10, part 1, 1969, 25–37.
5. Saheb K. Al-Saidy, Rabeaa G. Abtan, Haider J. Ali, More on MC-Functions, The Journal of the College of Basic Education (CBEJ), vol. 21, no. 89, 2015, 149–156.
6. A. A. Abdulah, R. G. A. Al-Aleyawee, Some new results on Shi arrangement, AIP Conference Proceedings, 2023, 2834(1), 080133.
7. R. G. Abtan, R. S. Haraj, Hyperfactored of the arrangements A(G24) and A(G27), Journal of Physics: Conference Series, 2021, 1818(1), 012144.
8. S. J. Kadhum, A. I. Abdul-Nabi, N. S. Jasim, Compute some concepts in P G(3, 8), Journal of Discrete Mathematical Sciences and Cryptography, 2022, 25(2), 599–604.
9. S. J. Kadhum, N. S. Jasim, A. I. Abdul-Nabi, Results for the (b, t)-blocking sets in P G(2, 8), AIP Conference Proceedings, 2023, 2845(1), 050044.
10. Auday Hekmat Mahmood, Maysaa Zaki Salman, A note on relatively commuting mappings of prime and semiprime rings, International Journal of Mathematics and Computer Science, 18(2023), no. 2, 153–162.
11. D. M. Hameed, Diagonal matrix of the tensor product (p ≥ 3 prime), Journal of Discrete Mathematical Sciences and Cryptography, 2025, 28(2), 457–461.
12. S. M. Salih, D. M. Hameed, Jordan permuting 3-left (resp. right) u-centralizers on prime semi-rings, Journal of Discrete Mathematical Sciences and Cryptography, 2025, 28(4), 1221–1226.
13. D. Mohamed Hameed, I. Zamil Mushtt, Invariant factors of the tensor product of (Ca3), IOP Conference Series: Materials Science and Engineering, 2020, 928(4), 042038.
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Published
2025-09-17
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Research Articles
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How to Cite
Zaki, M. ., Haraj, R. S., & Hameed, D. M. (2025). The third natural representation of the symmetric groups. Boletim Da Sociedade Paranaense De Matemática, 43, 1-7. https://doi.org/10.5269/bspm.78612
