Finite groups with many values in a column of the character table

2018 ◽  
Vol 17 (10) ◽  
pp. 1850196
Author(s):  
Pham Huu Tiep ◽  
Hung P. Tong-Viet
Keyword(s):  
Finite Groups ◽  
Character Table ◽  
Character Tables

In this paper, we classify all finite groups whose character tables have some column with pairwise distinct values.

A NOTE ON THE NUMBER OF ZEROS IN THE COLUMNS OF THE CHARACTER TABLE OF A GROUP

2012 ◽  
Vol 12 (02) ◽  
pp. 1250150 ◽  
Author(s):  
JINSHAN ZHANG ◽  
ZHENCAI SHEN ◽  
SHULIN WU
Keyword(s):  
Finite Groups ◽  
Irreducible Character ◽  
Conjugacy Classes ◽  
Character Table ◽  
Number Of Zeros

The finite groups in which every irreducible character vanishes on at most three conjugacy classes were characterized [J. Group Theory13 (2010) 799–819]. Dually, we investigate the finite groups whose columns contain a small number of zeros in the character table.

The Character Tables for SL(3, q), SU(3, q2), PSL(3, q), PSU(3, q2)

1973 ◽  
Vol 25 (3) ◽  
pp. 486-494 ◽  
Author(s):  
William A. Simpson ◽  
J. Sutherland Frame
Keyword(s):  
Character Table ◽  
Projective Group ◽  
Unitary Matrices ◽  
Character Tables

In this paper the character table of GL(3, q) (U(3, q2)), the group of all nonsingular n × n (unitary) matrices over GF(q) (GF(q2)), is used to obtain the character tables for the related subgroups SL(3, q), PSL(3, q) (SU(3, q2), PSU(3, q2)), the corresponding groups of matrices of determinant unity and the projective group respectively. There are very few abstract character tables which hold for entire families of groups. Such tables are of much greater value than tables for specific groups because, among other things, they enable one to discern various patterns common to the whole family.

scholarly journals Computing character tables of groups of type M.G.A

2011 ◽  
Vol 14 ◽  
pp. 173-178 ◽  
Author(s):  
Thomas Breuer
Keyword(s):  
Factor Group ◽  
Character Table ◽  
Character Tables

AbstractWe describe a method for constructing the character table of a group of type M.G.A from the character tables of the subgroup M.G and the factor group G.A, provided that A acts suitably on M.G. This simplifies and generalizes a recently published method.

Integral Group Rings of Finite Groups

1967 ◽  
Vol 10 (5) ◽  
pp. 635-642 ◽  
Author(s):  
B. Banaschewski
Keyword(s):  
Finite Groups ◽  
Character Table ◽  
Bilinear Forms ◽  
Group Rings ◽  
Integral Group ◽  
Linear Forms ◽  
Integral Group Rings

The main object of this paper is to show that the existence of a particular kind of isomorphism between the integral group rings of two finite groups implies that the groups themselves are isomorphic. The proof employs certain types of linear forms which are first discussed in general. These linear forms are in some way related to the bilinear forms used by Weidmann [3] in showing that groups with isomorphic character rings have the same character table, and a shorter and, in a sense, more natural proof of this result is included here as another application of these linear forms.

Classroom Friendly Method to Calculate Character Tables for Finite Groups

2020 ◽  
Vol 97 (7) ◽  
pp. 1915-1921
Author(s):  
Minhhuy Hô ◽  
León Francisco Alday Toledo ◽  
Roberto Bernal-Jaquez
Keyword(s):  
Finite Groups ◽  
Character Tables

scholarly journals The character table of a group of shape (2×2.G):2

2010 ◽  
Vol 13 ◽  
pp. 82-89
Author(s):  
R. W. Barraclough
Keyword(s):  
Character Table ◽  
Character Tables

AbstractWe use the technique of Fischer matrices to write a program to produce the character table of a group of shape (2×2.G):2 from the character tables ofG,G:2, 2.Gand 2.G:2.

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