Lifts and vertex pairs in solvable groups

2010/10/12 by James P. Cossey, Mark L. Lewis, Cossey, James P. +1
Mathematics · #20C15 #20C20 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20C15 #msc:20C20

paper · pdf · doi:10.48550/arxiv.1010.2380

arxiv created 2010/10/12 · arxiv updated 2010/10/13

Abstract

Suppose G is a p-solvable group, where p is odd. We explore the connection between lifts of Brauer characters of G and certain local objects in G, called vertex pairs. We show that if χ is a lift, then the vertex pairs of χ form a single conjugacy class. We use this to prove a sufficient condition for a given pair to be a vertex pair of a lift and to study the behavior of lifts with respect to normal subgroups.

Related

• Counting lifts of irreducible Brauer characters
• Counting lifts of Brauer characters
• Lifts of Brauer characters in characteristic two
• Navarro vertices and lifts in solvable groups
• The uniqueness of vertex pairs in π-separable groups