Armenian Journal of Mathematics, 16(3)
2024; 1–14
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Unit Group of the Group Algebra F q G L ( 2 , 7 )

Namatchivayam Umapathy Sivaranjani*, Elumalai Nandakumar, Gaurav Mittal, Rajendra Kumar

Received: 2024-12-03 · Published: 2024-03-13

© 2024 The Author(s) and the original publisher.

CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
Unit Group of the Group Algebra F q G L ( 2 , 7 )
Authors
Namatchivayam Umapathy Sivaranjani, Elumalai Nandakumar, Gaurav Mittal, Rajendra Kumar
Source journal
Armenian Journal of Mathematics, 16(3)
Published
2024-03-13
Licence
Creative Commons Attribution 4.0 International
Original
https://doi.org/10.52737/18291163-2024.16.3-1-14

Abstract

In this paper, we consider the general linear group GL(2,7)GL(2,7) of 2×22×2 invertible matrices over the finite field of order 77 and compute the unit group of the semisimple group algebra FqGL(2,7)FqGL(2,7), where FqFq is a finite field. For the computation of the unit group, we need the Wedderburn decomposition of FqGL(2,7)FqGL(2,7), which is determined by first computing the Wedderburn decomposition of the group algebra Fq(PSL(3,2)⋊C2)Fq(PSL(3,2)⋊C2). Here PSL(3,2)PSL(3,2) is the projective special linear group of degree 3 over a finite field of 2 elements.
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