Search results for "Solvable groups"

showing 2 items of 2 documents

The number of lifts of a Brauer character with a normal vertex

2011

AbstractIn this paper we examine the behavior of lifts of Brauer characters in p-solvable groups. In the main result, we show that if φ∈IBr(G) has a normal vertex Q and either p is odd or Q is abelian, then the number of lifts of φ is at most |Q:Q′|. As a corollary, we prove that if φ∈IBr(G) has an abelian vertex subgroup Q, then the number of lifts of φ in Irr(G) is at most |Q|.

CombinatoricsVertex (graph theory)LiftsAlgebra and Number TheoryBrauer's theorem on induced charactersCorollarySolvable groupAbelian groupFinite groupsSolvable groupsBrauer charactersMathematicsJournal of Algebra
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An answer to a question of Isaacs on character degree graphs

2006

Abstract Let N be a normal subgroup of a finite group G. We consider the graph Γ ( G | N ) whose vertices are the prime divisors of the degrees of the irreducible characters of G whose kernel does not contain N and two vertices are joined by an edge if the product of the two primes divides the degree of some of the characters of G whose kernel does not contain N. We prove that if Γ ( G | N ) is disconnected then G / N is solvable. This proves a strong form of a conjecture of Isaacs.

Normal subgroupCombinatoricsDiscrete mathematicsFinite groupMathematics(all)ConjectureGeneral MathematicsProjective charactersNormal subgroupsSolvable groupsCharacter degreesGraphMathematicsAdvances in Mathematics
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