6533b858fe1ef96bd12b6d31
RESEARCH PRODUCT
The number of lifts of a Brauer character with a normal vertex
Gabriel NavarroMark L. LewisJames P. Cosseysubject
CombinatoricsVertex (graph theory)LiftsAlgebra and Number TheoryBrauer's theorem on induced charactersCorollarySolvable groupAbelian groupFinite groupsSolvable groupsBrauer charactersMathematicsdescription
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|.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-02-01 | Journal of Algebra |