scholarly journals Existence of two conjugate classes of A5 within S6 by use of character table of S6

2013 ◽  
Vol 8 ◽  
pp. 1591-1596
Author(s):  
Abid Mahboob ◽  
Sajid Mahboob
Keyword(s):  
Character Table

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 largest Irreducible Character Degree of a Finite Group

1985 ◽  
Vol 37 (3) ◽  
pp. 442-451 ◽  
Author(s):  
David Gluck
Keyword(s):  
Finite Group ◽  
Irreducible Character ◽  
Abelian Subgroup ◽  
Character Degree ◽  
Character Table ◽  
Significant Information ◽  
Famous Theorem ◽  
Frobenius Reciprocity ◽  
A Finite Group ◽  
Irreducible Character Degree

Much information about a finite group is encoded in its character table. Indeed even a small portion of the character table may reveal significant information about the group. By a famous theorem of Jordan, knowing the degree of one faithful irreducible character of a finite group gives an upper bound for the index of its largest normal abelian subgroup.Here we consider b(G), the largest irreducible character degree of the group G. A simple application of Frobenius reciprocity shows that b(G) ≧ |G:A| for any abelian subgroup A of G. In light of this fact and Jordan's theorem, one might seek to bound the index of the largest abelian subgroup of G from above by a function of b(G). If is G is nilpotent, a result of Isaacs and Passman (see [7, Theorem 12.26]) shows that G has an abelian subgroup of index at most b(G)4.

The Fischer-Clifford Matrices and Character Table of a Maximal Subgroup of Fi24

2010 ◽  
Vol 17 (03) ◽  
pp. 389-414 ◽  
Author(s):  
Faryad Ali ◽  
Jamshid Moori
Keyword(s):  
Automorphism Group ◽  
Conjugacy Class ◽  
Maximal Subgroup ◽  
Computer Algebra ◽  
Character Table ◽  
Computer Algebra Systems ◽  
Split Extension ◽  
Sporadic Group ◽  
Local Subgroup ◽  
Fischer Group

The Fischer group [Formula: see text] is the largest 3-transposition sporadic group of order 2510411418381323442585600 = 222.316.52.73.11.13.17.23.29. It is generated by a conjugacy class of 306936 transpositions. Wilson [15] completely determined all the maximal 3-local subgroups of Fi24. In the present paper, we determine the Fischer-Clifford matrices and hence compute the character table of the non-split extension 37· (O7(3):2), which is a maximal 3-local subgroup of the automorphism group Fi24 of index 125168046080 using the technique of Fischer-Clifford matrices. Most of the calculations are carried out using the computer algebra systems GAP and MAGMA.

scholarly journals The character table of 2+1+22.Co2

2007 ◽  
Vol 315 (1) ◽  
pp. 301-325 ◽  
Author(s):  
Herbert Pahlings
Keyword(s):  
Character Table

scholarly journals On a Positivity Conjecture in the Character Table of $S_n$

10.37236/8186 ◽  
2019 ◽  
Vol 26 (1) ◽  
Author(s):  
Sheila Sundaram
Keyword(s):  
Lexicographic Order ◽  
Character Table ◽  
Power Sums ◽  
Special Cases ◽  
Schur Positive

In previous work of this author it was conjectured that the sum of power sums $p_\lambda,$ for partitions $\lambda$ ranging over an interval $[(1^n), \mu]$ in reverse lexicographic order, is Schur-positive. Here we investigate this conjecture and establish its truth in the following special cases: for $\mu\in [(n-4,1^4), (n)]$  or $\mu\in [(1^n), (3,1^{n-3})], $ or $\mu=(3, 2^k, 1^r)$ when $k\geq 1$ and $0\leq r\leq 2.$  Many new Schur positivity questions are presented.

A revision of male ants of the Malagasy region (Hymenoptera: Formicidae): Key to subfamilies and treatment of the genera of Ponerinae

Zootaxa ◽  
2007 ◽  
Vol 1654 (1) ◽  
pp. 21-40 ◽  
Author(s):  
MASASHI YOSHIMURA ◽  
BRIAN L. FISHER
Keyword(s):  
Character Table

Male-based keys to ant subfamilies and to the genera of Ponerinae in the Malagasy region (Madagascar, Mauritius, Reunion, Comores, and Seychelles) are presented. Seven subfamilies known from the Malagasy region in addition to an undetermined taxon are included in the subfamily key. All seven of the ponerine genera recorded in the region—Anochetus, Hypoponera, Leptogenys, Odontomachus, Pachycondyla, Platythyrea, and Ponera—are included. Diagnoses and remarks on the subfamily and genera within Ponerinae, and a character table for the ponerine genera, are given. The males of the seven ponerine genera are illustrated.

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.

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