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ISSN: 2321-9653
Estd : 2013
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Ijraset Journal For Research in Applied Science and Engineering Technology

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A Note on the Wedderburn Decomposition and Unit Group of the Semisimple Group Algebra FpSn

Authors: Shubham Mittal

DOI Link: https://doi.org/10.22214/ijraset.2022.46253

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Abstract

In this short note, we give an algorithm to compute the unit group of a semisimple group algebra for any . To show the practicality of the algorithm, we explicitly find the unit groups of the semisimple group algebras , , and .

Introduction

References

[1] G. K. Bakshi, S. Gupta, I. B. S. Passi, “The algebraic structure of finite metabelian group algebras”, Comm. Algebra, 43(1), (2015), 2240-2257. [2] R. A. Ferraz, “Simple components of the center of ”, Comm. Algebra, 36(9), 3191-3199, 2008. [3] W. Fulton, Young tableaux, with applications to representation theory and geometry, Cambridge University Press, 1997. [4] G. D. James, The representation theory of the symmetric groups, Springer, 1978. [5] M. Khan, R. K. Sharma, J. B. Srivastava, “The unit group of ”, Acta Math. Hungar., 118 (1-2), 105-113, 2008. [6] C. P. Milies, S. K. Sehgal, An introduction to group rings, Kluwer Acad. Pub., 2002. [7] G. Mittal, R. K. Sharma, “On unit group of finite group algebras of non-metabelian groups upto order 72”, Math. Bohemica, 146(4), 429-455, 2021. [8] G. Mittal, R. K. Sharma, “Unit group of semisimple group algebras of some non-metabelian groups of order 120”, Asian-European J. Math., 15(3), 2250059, 2022. [9] G. Mittal, R. K. Sharma, “Computation of Wedderburn decomposition of groups algebras from their subalgebra”, Bull. Korean Math. Soc., 59(3), 781-787 2022. [10] G. Mittal, R. K. Sharma, “Wedderburn decomposition of a semisimple group algebra from a subalgebra of factor group of ”, Int. Elect. J. Algebra, 32, 91-100, 2022. [11] G. Mittal, R. K. Sharma, “On unit group of finite group algebras of non-metabelian groups of order 108”, J. Algebra Comb. Discrete Appl., 8(2), 59-71, 2021. [12] B. Sagan, The Symmetric Group. Representations, Combinatorial Algorithms, and Symmetric Functions, Springer-Verlag, 2001. [13] M Sahai, SF Ansari , “Unit groups of the finite group algebras of generalized quaternion groups”, J. Algebra Its Appl., , . [14] R. K. Sharma, J. B. Srivastava, M. Khan, “The unit group of ”, Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis, 23(2), 129-142, 2007. [15] R. K. Sharma, G. Mittal, “ Unit group of semisimple group algebra ”, Math. Bohemica, 147(1), 1-10, 2022.

Copyright

Copyright © 2022 Shubham Mittal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

IJRASET46253

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Paper Id : IJRASET46253

Publish Date : 2022-08-09

ISSN : 2321-9653

Publisher Name : IJRASET

DOI Link : Click Here