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On generalized Gagola characters
We give a natural generalization of the Gagola characters of finite groups from the aspect of Galois conjugation of characters, and then present some...
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A characterization of almost simple K 3-groups
It is a well-known fact that characters of a finite group can give important information about the group’s structure. Also it was proved by the third...
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A new characterization for the simple group PSL(2, p 2) by order and some character degrees
Let G be a finite group and p a prime number. We prove that if G is a finite group of order |PSL(2, p 2 )| such that G has an irreducible character of...
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Finite groups with an irreducible character of large degree
Let G be a finite group and d the degree of a complex irreducible character of G , then write | G | = d ( d + e ) where e is a nonnegative integer. We...
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Finite Groups with a Given Set of Character Degrees
Let G be a finite group with {1, q , r , qm , q 2 m , rqm } as the character degree set, where r and q are distinct primes and m >1 is an integer not...
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Nonsolvable D 2-groups
Let G be a finite group. Let Irr 1 ( G ) be the set of nonlinear irreducible characters of G and cd 1 ( G ) the set of degrees of the characters in Irr 1 ( G )....
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Broué’s Perfect Isometry Conjecture Holds for the Double Covers of the Symmetric and Alternating Groups
In O. Brunat and J. Gramain (
2014 ) recently proved that any two blocks of double covers of symmetric groups are Broué perfectly isometric provided... -
Graphs of nonsolvable groups with four degree-vertices
Let G be a finite group. The degree (vertex) graph Γ( G ) attached to G is a character degree graph. Its vertices are the degrees of the nonlinear...
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On the Existence of Johnson Polynomials for Nilpotent Groups
Let G be a finite group. We say that G has a Johnson polynomial if there exists a polynomial f ( x ) ∈ ℤ[ x ] and a character χ ∈ Irr( G ) so that f ( χ )...
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Fusion Procedure for Degenerate Cyclotomic Hecke Algebras
The primitive idempotents of the degenerate cycloctomic Hecke algebras are derived by consecutive evaluations of a certain rational function. This...
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Class product and character product
For each finite group G , the product in the group ring of all the conjugacy class sums is a positive integer multiple of the sum of the elements in a...
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Rational permutation groups containing a full cycle
A finite group whose irreducible complex characters are rational valued is called a rational group. Thus, G is a rational group if and only if N ...
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Classification of solvable groups possessing a unique nonlinear non-faithful irreducible character
In this note, we study finite groups possessing exactly one nonlinear non-faithful irreducible character. Our main result is to classify solvable...
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A new characterization of Mathieu-groups by the order and one irreducible character degree
The main aim of this article is to characterize the finite simple groups by less character quantity. In fact, we show that each Mathieu -group G can...
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A note on the basic Morita equivalences
Let G and G ′ be two finite groups, and p be a prime number. k is an algebraically closed field of characteristic p . We denote by b and b ′ the block...
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3-Blocks with Abelian defect groups isomorphic to \(Z_{3^m } \times Z_{3^n } \)
Let G be a finite group and let p be a fixed prime number. Let B be a p -block of G with defect group D . In this paper, we give results on 3-blocks...
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Mackey’s theory of \({\tau}\)-conjugate representations for finite groups
The aim of the present paper is to expose two contributions of Mackey, together with a more recent result of Kawanaka and Matsuyama, generalized by...
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Finite Groups with K 4-Free Prime Graphs
Let G be a finite group and let cd( G ) be the set of all complex irreducible character degrees of G . Let ρ ( G ) be the set of all primes dividing some...