Corpus ID: 235436205

Finite non-solvable groups whose real degrees are prime-powers

@inproceedings{Bonazzi2021FiniteNG,
  title={Finite non-solvable groups whose real degrees are prime-powers},
  author={Lorenzo Bonazzi},
  year={2021}
}
We present a description of non-solvable groups in which all real irreducible character degrees are prime-power numbers. 

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SHOWING 1-10 OF 18 REFERENCES
Groups whose real irreducible characters have degrees coprime to p
Abstract In this paper we study groups for which every real irreducible character has degree not divisible by some given odd prime p .
Finite groups with real-valued irreducible characters of prime degree
Abstract In this paper we describe the structure of finite groups whose real-valued nonlinear irreducible characters have all prime degree. The more general situation in which the real-valuedExpand
Rational irreducible characters and rational conjugacy classes in finite groups
We prove that a finite group G has two rational-valued irreducible characters if and only if it has two rational conjugacy classes, and determine the structure of any such group. Along the way weExpand
Finite Group Theory
In this window, all groups are assumed finite. Here we collect a number of results that play a significant role in the book (further material of an elementary nature that we sometimes take forExpand
Character Theory of Finite Groups
1. (i) Suppose K is a conjugacy class of Sn contained in An; then K is called split if K is a union of two conjugacy classes of An. Show that the number of split conjugacy classes contained in An isExpand
Real characters and degrees
Several classical theorems on character degrees are revisited from the point of view of the real characters.
Primes dividing the degrees of the real characters
Let G be a finite group and let Irr(G) denote the set of all complex irreducible characters of G. The Ito–Michler Theorem asserts that if a prime p does not divide the degree of any χ $$\in$$ Irr(G)Expand
Character degree graphs that are complete graphs
Let G be a finite group, and write cd(G) for the set of degrees of irreducible characters of G. We define F(G) to be the graph whose vertex set is cd(G) - {1}, and there is an edge between a and b ifExpand
NOTES ON FINITE SIMPLE GROUPS WHOSE ORDERS HAVE THREE OR FOUR PRIME DIVISORS
Based on the prime graph of a finite group, its order can be divided into a product of some co-prime positive integers. These integers are called order components of this group. If there existExpand
Nearly odd-order and nearly real finite groups
Two families of groups close to groups of odd order, and two families of groups close to real groups will be described. The first two are the family of finite groups in which all real irreducibleExpand
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