Title: The Fitting subgroup, <i>p</i>‐length, derived length and character table
Abstract: Abstract For a character χ of a finite group G , the number is called the codegree of χ. Let N be a normal subgroup of G and set Let p be a prime. In this paper, we first show that if for two distinct prime divisors p and q of , divides none of the codegrees of elements of , then and N is either p ‐solvable or q ‐solvable. Next, we classify the finite groups with exactly one irreducible character of the codegree divisible by p and, also finite groups whose codegrees of irreducible characters which are divisible by p are equal. Then, we prove that p ‐length of a finite p ‐solvable group is not greater than the number of the distinct codegrees of its irreducible characters which are divisible by p . Finally, we consider the case when the codegree of every element of is square‐free.
Publication Year: 2020
Publication Date: 2020-11-26
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 9
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