Groups with some cube-free irreducible character co-degrees
R Bahramian, N Ahanjideh… - Communications in …, 2023 - Taylor & Francis
R Bahramian, N Ahanjideh, AR Naghipour
Communications in Algebra, 2023•Taylor & FrancisFor a character χ of a finite group G, the number cod (χ)=[G: ker χ] χ (1) is called the co-
degree of χ. Let n≥ 2 be an integer and Irr (G| Fit (G)) denote the set of irreducible
characters whose kernels do not contain Fit (G). In this paper, we show that if G is solvable
and pn+ 1∤ cod (χ) for every prime divisor p of| G| and every χ∈ Irr (G| Fit (G)), then the
derived length of G is at most 2 log 2 (n)+ log 2 (n− 1)+ 4. Then, we classify the finite non-
solvable groups with non-trivial Fitting subgroups such that the co-degrees of their …
degree of χ. Let n≥ 2 be an integer and Irr (G| Fit (G)) denote the set of irreducible
characters whose kernels do not contain Fit (G). In this paper, we show that if G is solvable
and pn+ 1∤ cod (χ) for every prime divisor p of| G| and every χ∈ Irr (G| Fit (G)), then the
derived length of G is at most 2 log 2 (n)+ log 2 (n− 1)+ 4. Then, we classify the finite non-
solvable groups with non-trivial Fitting subgroups such that the co-degrees of their …
Abstract
For a character χ of a finite group G, the number is called the co-degree of χ. Let be an integer and denote the set of irreducible characters whose kernels do not contain . In this paper, we show that if G is solvable and for every prime divisor p of and every , then the derived length of G is at most . Then, we classify the finite non-solvable groups with non-trivial Fitting subgroups such that the co-degrees of their irreducible characters whose kernels do not contain the Fitting subgroups are cube-free.
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