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Nonsolvable Groups with Three Nonlinear Irreducible Character Codegrees
For an irreducible character χ of a finite group G , the codegree of χ is defined as ∣ G : ker( χ )∣/ χ (1). In this paper, the authors determine finite...
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Results related to Huppert’s ϱ-σ conjecture
We improve a few results related to Huppert’s ϱ - σ conjecture. We also generalize a result about the covering number of character degrees to arbitrary...
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Finite Groups with Some Bounded Codegrees
For a character χ of a finite group G , the number cod( χ )≔ ∣ G : ker( χ )∣/ χ (1) is called the codegree of χ . In this paper, we give a solvability...
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A New Characterization of Sporadic Simple Group M22 via Its Vanishing Elements
For a finite group G , a vanishing element of G is an element g ∈ G such that χ ( g ) = 0 for some irreducible complex character χ of G . Denote by π e ( G )...
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Normal Sylow subgroups and monomial Brauer characters
Let G be a finite group, p be a prime divisor of | G |, and P be a Sylow p -subgroup of G . We prove that P is normal in a solvable group G if | G : ker φ |
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Nonsolvable groups whose irreducible character degrees have special 2-parts
Let G be a nonsolvable group and Irr( G ) the set of irreducible complex characters of G . We consider the nonsolvable groups whose character degrees...
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On Covering Number of Groups with Trivial Fitting Subgroup
Let G be a finite group and S be a subset of Irr( G ). If for every prime divisor p of ∣ G ∣ there is a character χ in S such that p divides χ (1), S is...
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On supercharacter theoretic generalizations of monomial groups and Artin’s conjecture
We extend the notions of quasi-monomial groups and almost monomial groups in the framework of supercharacter theories, and we study their connection...
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A Solvability Criterion for Finite Groups Related to Character Degrees
Let m > 1 be a fixed positive integer. In this paper, we consider finite groups each of whose nonlinear character degrees has exactly m prime...
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Finite p-groups with Few Kernels of Nonlinear Irreducible Characters
Let G be a finite nonabelian group and Kern( G ) the set of kernels of nonlinear irreducible characters of G . In this paper, finite p -groups G with...
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Finite groups with two rows which differ in only one entry in character tables
Let G be a finite group. If G has two rows which differ in only one entry in the character table, we call G an RD1-group. We investigate the...
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On Quasi Steinberg Characters of Complex Reflection Groups
Let G be a finite group and p be a prime number dividing the order of G . An irreducible character χ of G is called a quasi p -Steinberg character if χ (
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Reflection Representations of Coxeter Groups and Homology of Coxeter Graphs
We study and classify a class of representations (called generalized geometric representations) of a Coxeter group of finite rank. These...
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A Note on the Rational Non-linear Characters of Groups
We study finite groups with rational valued non-linear characters and obtain the structure of these types of groups with derived subgroup of prime...
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Extensions of Theorems of Gaschütz, Žmud′ and Rhodes on Faithful Representations
Gaschütz (1954) proved that a finite group G has a faithful irreducible complex representation if and only if its socle is generated by a single...
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Zeros of Monomial Brauer Characters
Let G be a finite group and p be a fixed prime. A p -Brauer character of G is said to be monomial if it is induced from a linear p -Brauer character of...
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Sylow Subgroups and Fusion of Characters
Suppose that P is a Sylow p -subgroup of G . We study irreducible characters of P that are constant on G -fused classes.