Unit groups of semisimple group algebras of groups up to order 180
N. Abhilashan1295@srmist.edu.inDepartment of MathematicsCollege of Engineering and TechnologySRM Institute of Science & TechnologyKattankulathur, Tamil Nadu, 603203, IndiaView full profile → , *E. NandakumarCorresponding authornanda1611@gmail.comDepartment of MathematicsCollege of Engineering and TechnologySRM 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 MathematicsIndian Institute of TechnologyDelhi, 110016, IndiaView full profile →
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- Received:
- 16 Aug 2023
- Published Online:
- 30 Sep 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1858
- Pages:
- 1383–1404
Abstract
Keywords
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References
[1] N. Abhilash, E. Nandakumar, R. K. Sharma, G. Mittal, Structure of the unit group of the group algebras of NMG of order 128, Preprint (2023).
[2] N. Abhilash, E. Nandakumar, R. K. Sharma, G. Mittal, On the unit group of the SGA of groups up to order 144, Preprint (2023).
[3] N. Abhilash, E. Nandakumar, G. Mittal, R. K. Sharma, Units of the SGA of groups of order 162, Preprint (2023).
[4] N. Arvind, S. Panja, Unit group of some finite semi-simple group algebras, J. Egypt. Math. Soc., 30, Article No. 17 (2022).
[5] G. K. Bakshi, S. Gupta, I. B. S. Passi, The algebraic structure of finite metabelian group algebras, Comm. Algebra, 43(1), 2240-2257 (2015).
[6] C. Dietzel, G. Mittal, Summands of finite group algebras, Czech. Math. J., 71, 1011-1014 (2021).
[7] R. Ferraz, Simple components of center of FG/J(FG), Comm. Algebra, 36(9), 3191- 3199 (2008).
[8] W. Gao, A. Geroldinger, F. Halter- Koch, Group algebras of finite abelian groups and their applications to combinatorial problems, Rocky Mountain J. Math., 39, 805-823 (2008).
[9] J. Gildea, The structure of the unit group of the group algebra F2kA4, Czechoslovak Math. J., 61, 531-539 (2011).
[10] T. Hurley, Group rings and rings of matrices, Int. J. Pure Appl. Math., 31(3), 319-335 (2006).
[11] T. Hurley, Convolutional codes from units in matrix and group rings, Int. J. Pure Appl. Math., 50(3), 431-463 (2009).
[12] M. Khan, R. K. Sharma, J. Srivastava, The unit group of FS4, Acta Math. Hungar., 118, 105-113 (2008).
[13] S. Maheshwari, R. K. Sharma, The unit group of the group algebra FqSL(2, Z3) J. Algebra Comb. Discrete Appl., 3(1), 1-6 (2015).
[14] N. Makhijani, R. K. Sharma, J. Srivastava, A note on the structure of FpkA5/J(FpkA5), Acta Sci. Math. (Szeged), 82, 29-43 (2016).
[15] Manju Pruthi, Sudesh, Idempotents in the group algebra of dihedral groups, Journal of Information and Optimization Sciences, 39:2, 461-465 (2018).
[16] C. P. Miles, S. K. Sehgal, An introduction to group rings, Kluwer Academic Publishers, Dordrcht (2002).
[17] G. Mittal, R. K. Sharma, On unit group of finite group algebras of NMG up to order 72, Math. Bohemica, 146(4), 1-27 (2021).
[18] G. Mittal, R. K. Sharma, On unit group of finite group algebras of NMG of order 108, J. Algebra Comb. Discrete Appl., 8(2), 59-71 (2021).
[19] G. Mittal, S. Kumar, S. Narain, S. Kumar, Group ring based public key cryptosystems, J. Disc. Math. Sci. Crypt., 25(6), 1683-1704 (2022).
[20] G. Mittal, R. K. Sharma, Unit group of SGA of some NMG of order 120, Asian-European J. Math., 15(3), 2250059 (2022).
[21] G. Mittal, R. K. Sharma, The unit groups of SGA of some NMG of order 144, Math. Bohemica, Online first (2022).
[22] G. Mittal, R. K. Sharma, WD of a semisimple group algebra FqG from a subalgebra of factor group of G, Int. Elect. J. Algeb., 32, 91-100 (2022).
[23] G. Mittal, R. K. Sharma, Computation of WD of groups algebras from their subalgebra, Bull. Korean Math. Soc., 59(3), 781-787 (2022).
[24] G. Mittal, R. K. Sharma, Computation of the WD of SGA of groups up to order 120, Preprint (2022).
[25] N. Arvind, S. Panja, The unit group of KqSL(3,2), p > 11, Arxiv (2021).
[26] G. Pazderski, The orders to which only belong metabelian groups, Math. Nachr., 95, 7-16 (1980).
[27] R. K. Sharma, G. Mittal, On the unit group of a semisimple group algebra FqSL(2, Z5) Math. Bohemica, 147(1), 1-10 (2022).
[28] R. K. Sharma, J. B. Srivastava, M. Khan, The unit group of FA4, Publ. Math. Debrecen, 71(1-2), 21-26 (2007).
[29] R. K. Sharma, J. B. Srivastava, M. Khan, The unit group of FS3, Acta Math. Acad. Paedagog. Nyhzi., 23(2), 129-142 (2007).
[30] R. K. Sharma, P. Yadav, The unit group of ZpQ8, Algebras Groups Geom., 25(4), 425-429 (2008).
[31] Re’em Waxman, On the Wedderburn component of a group algebra, https://math.stackexchange.com/q/4682495.
[32] G. Tang, Y. Wei, Y. Li, Units group of group algebras of some small groups, Czechoslovak Math. J., 64(1), 149-157 (2014).
