On p-parts of Brauer character degrees and p-regular conjugacy class sizes of finite groups

2020 ◽  
Vol 560 ◽  
pp. 296-311
Author(s):  
Christine Bessenrodt ◽  
Yong Yang
Keyword(s):  
Conjugacy Class ◽  
Finite Groups ◽  
Character Degrees ◽  
Conjugacy Class Sizes ◽  
Brauer Character

ON CONJUGACY CLASS SIZES AND CHARACTER DEGREES OF FINITE GROUPS

2013 ◽  
Vol 13 (02) ◽  
pp. 1350100 ◽  
Author(s):  
GUOHUA QIAN ◽  
YANMING WANG
Keyword(s):  
Finite Group ◽  
Conjugacy Class ◽  
Nilpotent Group ◽  
Finite Groups ◽  
Prime Power ◽  
P Element ◽  
Character Degrees ◽  
Prime Power Order ◽  
Conjugacy Class Sizes ◽  
A Finite Group

Let p be a fixed prime, G a finite group and P a Sylow p-subgroup of G. The main results of this paper are as follows: (1) If gcd (p-1, |G|) = 1 and p2 does not divide |xG| for any p′-element x of prime power order, then G is a solvable p-nilpotent group and a Sylow p-subgroup of G/Op(G) is elementary abelian. (2) Suppose that G is p-solvable. If pp-1 does not divide |xG| for any element x of prime power order, then the p-length of G is at most one. (3) Suppose that G is p-solvable. If pp-1 does not divide χ(1) for any χ ∈ Irr (G), then both the p-length and p′-length of G are at most 2.

On Graphs Associated with Character Degrees and Conjugacy Class Sizes of Direct Products of Finite Groups

2015 ◽  
Vol 58 (1) ◽  
pp. 105-109 ◽  
Author(s):  
Samaneh Hossein-Zadeh ◽  
Ali Iranmanesh ◽  
Mohammad Ali Hosseinzadeh ◽  
Mark L. Lewis
Keyword(s):  
Conjugacy Class ◽  
Direct Product ◽  
Finite Groups ◽  
Character Degrees ◽  
Direct Products ◽  
Conjugacy Class Sizes ◽  
Vertex Graph ◽  
The Common ◽  
Positive Integers

Abstract.The prime vertex graph, Δ(X), and the common divisor graph, Γ(X), are two graphs that have been deûned on a set of positive integers X. Some properties of these graphs have been studied in the cases where either X is the set of character degrees of a group or X is the set of conjugacy class sizes of a group. In this paper, we gather some results on these graphs arising in the context of direct product of two groups.

Conjugacy class sizes and solvability of finite groups

2013 ◽  
Vol 123 (2) ◽  
pp. 239-244 ◽  
Author(s):  
QINHUI JIANG ◽  
CHANGGUO SHAO
Keyword(s):  
Conjugacy Class ◽  
Finite Groups ◽  
Conjugacy Class Sizes
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