Isomorphism Problem for Almost Simple Linear Groups

被引：0

作者：

Shirjian, Farrokh ^{[1
]}

Iranmanesh, Ali ^{[1
]}

Shafiei, Farideh ^{[2
]}

机构：

[1] Tarbiat Modares Univ, Fac Math Sci, Dept Pure Math, Tehran, Iran

[2] Inst Res Fundamental Sci IPM, Sch Math, Tehran, Iran

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2022年 / 19卷 / 06期

基金：

美国国家科学基金会;

关键词：

Complex group algebras; character degrees; almost simple groups; POWER DEGREE REPRESENTATIONS; COMPLEX GROUP-ALGEBRAS; DOUBLE COVERS; CHARACTERS;

D O I：

10.1007/s00009-022-02172-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to contribute to the Isomorphism Problem of complex group algebras which, informally, asks how much the complex group algebra of a finite group G over C know about the structure of the group. In this paper, we show that finite groups G, where PSLn(q) <= G <= PGL(n)(q), are uniquely determined (up to isomorphism) by the structure of their complex group algebras. This completes the studies initiated by Shirjian and Iranmanesh (Commun Algebra 46(2):552-573, 2018) and extends the main result of Bessenrodt et al. (Algebra Number Theory 9(3):601-628, 2015) to the family of almost simple linear groups of arbitrary large rank.

引用

页数：20

共 32 条

[1]

[Anonymous], 1892, MONATSH MATH PHYS, DOI DOI 10.1007/BF01692444

[2] Prime power degree representations of the symmetric and alternating groups [J].