On the unit group of the semisimple group algebra KqGL(2, ℤ5)
N. U. Sivaranjanisn0926@srmist.edu.inDepartment of Mathematics College of Engineering and Technology SRM Institute of Science & TechnologyKattankulathur, Tamil Nadu, 603203, IndiaView full profile → , *E. NandakumarCorresponding authornanda1611@gmail.comDepartment of Mathematics College of Engineering and Technology SRM Institute of Science & TechnologyKattankulathur, Tamil Nadu, 603203, IndiaView full profile → , G. Mittalgaurav.mittaltwins@yahoo.comDefence Research and Development Organization Near Metcalfe HouseDelhi, 110054, IndiaView full profile → , R. K. Sharmarksharmaiitd@gmail.comDepartment of Mathematics Indian Institute of TechnologyDepartment of Mathematics Indian Institute of Technology DelhiNew Delhi, 110016, IndiaView full profile →
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- Received:
- 05 Apr 2023
- Published Online:
- 27 Feb 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1733
- Pages:
- 121–134
Abstract
Keywords
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References
[1] N. Arvind, S. Panja, The unit group of arXiv:2106.07261.
[2] Y. Bai, Y. Li, J. Peng, Unit groups of finite group algebras of abelian groups of order 17 to 20, AIMS Mathematics 6, 7305-7317 (2021).
[3] G. K. Bakshi, S. Gupta, I. B. S. Passi, The algebraic structure of finite metabelian group algebras, Comm. Algebra 43, 2240-2257 (2015).
[4] A. Bovdi, J. Kurdics, Lie properties of the group algebra and the nilpotency class of the group of units, J. Algebra 212, 28-64 (1999).
[5] C. Dietzel, G. Mittal, Summands of finite group algebras, Czech. Math. J. 71, 1011-1014 (2021).
[6] R. Ferraz, Simple components of center of Comm. Algebra 36, 3191-3199 (2008).
[7] M. Hill, Irreducible representation of link: www.math.harvard.edu/archive/ 126_fall_98/papers/mahill.pdf.
[8] T. Hurley, Convolutional codes from units in matrix and group rings, Int. J. Pure Appl. Math. 50, 431-463 (2009).
[9] M. Khan, R. K. Sharma, J. Srivastava, The unit group of Acta Math. Hungar. 118, 105-113 (2008).
[10] S. Maheshwari, R. K. Sharma, The unit group of the group algebra J. Algebra Comb. Discrete Appl. 3, 1-6 (2015).
[11] N. Makhijani, R. K. Sharma, The unit group of algebra of circulant matrices, Int. J. Group Theory 3, 13-16 (2014).
[12] N. Makhijani, R. K. Sharma, J. B. Srivastava, The unit group of some special semisimple group algebras, Quaest. Math. 39, 9-28 (2016).
[13] C. P. Milies, S. K. Sehgal, An Introduction to group rings, Springer Dordrecht (2002).
[14] G. Mittal, R. K. Sharma, On unit group of finite group algebras of non-metabelian groups up to order 72, Math. Bohemica 146, 1-27 (2021).
[15] G. Mittal, R. K. Sharma, Wedderburn decomposition of a semisimple group algebra from a subalgebra of factor group of G, Int. Elect. J. Algebra 32, 91-100 (2022).
[16] G. Mittal, R. K. Sharma, Unit group of semisimple group algebras of some non-metabelian groups of order 120, Asian-European J. Math. 15, 2250059 (2022).
[17] G. Mittal, R. K. Sharma Computation of Wedderburn decomposition of groups algebras from their subalgebra, Bull. Korean Math. Soc. 59, 781-787 (2022).
[18] R. K. Sharma, G. Mittal, On the unit group of a semisimple group algebra Math. Bohemica 147, 1-10 (2022).
[19] R. K. Sharma, J. B. Srivastava, M. Khan, The unit group of Acta Math. Acad. Paedagog. Nyhazi. (N.S.) 23, 129-142 (2007).
[20] R. K. Sharma, P. Yadav, Unit group of algebra of circulant matrices, Int. J. Group Theory 2, 1-6 (2013).
[21] G. Tang, Y. Wei, Y. Li, Unit groups of group algebras of some small groups, Czech. Math. J. 64, 149-157 (2014).




