Character table of the simple group of order 168

2001 ◽  
pp. 311-321
Keyword(s):  
Simple Group ◽  
Character Table

The Character Table of Fischer's Simple Group, M(23)

1974 ◽  
Vol 28 (126) ◽  
pp. 660
Author(s):  
David C. Hunt
Keyword(s):  
Simple Group ◽  
Character Table

scholarly journals Characterization of a family of simple groups by their character table

1977 ◽  
Vol 24 (3) ◽  
pp. 296-304 ◽  
Author(s):  
Marcel Herzog ◽  
David Wright
Keyword(s):  
Conjugacy Class ◽  
Simple Group ◽  
Character Table ◽  
Simple Groups

AbstractThe paper establishes a method for bounding the 2-rank of a simple group with one conjugacy class of involutions, by means of its character table. For many groups of 2-rank ≦ 4, this bound is shown to be exact. The main result is that the simple groups G2(q),(q,6) = 1, are characterized bv their character table.

Another Existence and Uniqueness Proof for the Higman–Sims Simple Group

2005 ◽  
Vol 12 (03) ◽  
pp. 369-398
Author(s):  
Gerhard O. Michler ◽  
Andrea Previtali
Keyword(s):  
Automorphism Group ◽  
Simple Group ◽  
Existence And Uniqueness ◽  
Short Proof ◽  
Conjugacy Classes ◽  
Character Table ◽  
Sporadic Simple Group ◽  
Uniqueness Criterion ◽  
Generators And Relations ◽  
Uniqueness Proof

In this article, we give a short proof for the existence and uniqueness of the Higman–Sims sporadic simple group 𝖧𝖲 by means of the first author's algorithm [17] and uniqueness criterion [18], respectively. We realize 𝖧𝖲 as a subgroup of GL 22(11), and determine its automorphism group Aut (𝖧𝖲). We also give a presentation for Aut (𝖧𝖲) in terms of generators and relations. Furthermore, the character table of 𝖧𝖲 is determined and representatives of its conjugacy classes are given as short words in its generating matrices inside GL 22(11).

The Fischer–Clifford Matrices of a Maximal Subgroup of the Sporadic Simple Group of Held

2007 ◽  
Vol 14 (01) ◽  
pp. 135-142 ◽  
Author(s):  
Faryad Ali
Keyword(s):  
Simple Group ◽  
Computer Algebra ◽  
Local Structure ◽  
Computer Algebra System ◽  
Conjugacy Classes ◽  
Character Table ◽  
Maximal Subgroups ◽  
Split Extension ◽  
Sporadic Simple Group ◽  
Held Group

The Held group He discovered by Held [10] is a sporadic simple group of order 4030387200 = 210.33.52.73.17. The group He has 11 conjugacy classes of maximal subgroups as determined by Butler [5] and listed in the 𝔸𝕋𝕃𝔸𝕊. Held himself determined much of the local structure of He as well as the conjugacy classes of its elements. Thompson calculated the character table of He . In the present paper, we determine the Fischer–Clifford matrices and hence compute the character table of the non-split extension 3·S7, which is a maximal subgroups of He of index 226560 using the technique of Fischer–Clifford matrices. Most of the computations were carried out with the aid of the computer algebra system 𝔾𝔸ℙ.

O'NAN GROUP UNIQUELY DETERMINED BY THE CENTRALIZER OF A 2-CENTRAL INVOLUTION

2007 ◽  
Vol 06 (01) ◽  
pp. 135-171 ◽  
Author(s):  
GERHARD O. MICHLER ◽  
ANDREA PREVITALI
Keyword(s):  
Simple Group ◽  
Existence And Uniqueness ◽  
Conjugacy Classes ◽  
Character Table ◽  
Permutation Representation ◽  
Defining Relations ◽  
New Methods ◽  
Uniqueness Proof ◽  
Janko Group

In this paper we give a self-contained existence and uniqueness proof for the sporadic O'Nan group ON by showing that it is uniquely determined up to isomorphism by the centralizer H of a 2-central involution z. We establish for such a simple group G a presentation in terms of generators and defining relations and a faithful permutation representation of degree 2.624.832 with a uniquely determined stabilizer isomorphic to the small sporadic Janko group J1. We also calculate its character table by new methods and determine a system of representatives of the conjugacy classes of G.

scholarly journals Character Table Groups and Extracted Simple and Cyclic Polygroups

2020 ◽  
Vol 26 (1) ◽  
pp. 22-36
Author(s):  
Sara Sekhavatizadeh ◽  
Mohammad Mehdi Zahedi ◽  
Ali Iranmanesh
Keyword(s):  
Finite Group ◽  
Simple Group ◽  
Character Table ◽  
Finite Period ◽  
A Finite Group ◽  
Single Power ◽  
Complex Characters

Let G be a finite group and \hat{G} be the set of all irreducible complex characters of G. In this paper, we consider \hat{G}, * as a polygroup, where for each chi_i ,chi_j in \hat{G} the product \chi _{i} * \chi_{j} is the set of those irreducible constituents which appear in the element-wise product \chi_{i} \chi_{j}. We call that \hat{G} simple if it has no proper normal subpolygroup and show that if \hat{G} is a single power cyclic polygroup, then \hat{G} is a simple polygroup and hence \hat{S}_{n} and \hat{A}_{n} are simple polygroups. Also, we prove that if G is a non-abelian simple group, then \hat{G} is a single power cyclic polygroup. Moreover, we classify \hat{D}_{2n} for all n. Also, we prove that \hat{T}_{4n} and \hat{U}_{6n} are cyclic polygroups with finite period.

scholarly journals The intersection graph of a finite simple group has diameter at most 5

2021 ◽  
Author(s):  
Saul D. Freedman
Keyword(s):  
Simple Group ◽  
Upper Bound ◽  
Finite Simple Group ◽  
Unitary Groups ◽  
Intersection Graph ◽  
Monster Group ◽  
Prime Dimension

AbstractLet G be a non-abelian finite simple group. In addition, let $$\Delta _G$$ Δ G be the intersection graph of G, whose vertices are the proper non-trivial subgroups of G, with distinct subgroups joined by an edge if and only if they intersect non-trivially. We prove that the diameter of $$\Delta _G$$ Δ G has a tight upper bound of 5, thereby resolving a question posed by Shen (Czechoslov Math J 60(4):945–950, 2010). Furthermore, a diameter of 5 is achieved only by the baby monster group and certain unitary groups of odd prime dimension.

scholarly journals Groups with the Same Prime Graph as the Simple Group D n (5)

2014 ◽  
Vol 66 (5) ◽  
pp. 666-677
Author(s):  
A. Babai ◽  
B. Khosravi
Keyword(s):  
Simple Group ◽  
Prime Graph ◽  
Group D

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.

Sign in / Sign up

Export Citation Format

Share Document