Unit Group of the Group Algebra FqGL(2, 7)

被引：0

作者：

Sivaranjani, N. U. ^{[1
]}

Nandakumar, E. ^{[1
]}

Mittal, G. ^{[2
]}

Sharma, R. K. ^{[3
]}

机构：

[1] SRM Inst Sci & Technol, Coll Engn & Technol, Dept Math, Kattankulathur 603203, Tamil Nadu, India

[2] Def Res & Dev Org, New Delhi 110054, India

[3] Indian Inst Technol Delhi, Dept Math, Delhi 110016, India

来源：

ARMENIAN JOURNAL OF MATHEMATICS | 2024年 / 16卷 / 03期

关键词：

Unit Group; Group Algebra; General Linear Group; Wedder- burn Decomposition;

D O I：

10.52737/18291163-2024.16.3-1-14

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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

引用

页码：1 / 14

页数：14

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