Lifts of Brauer characters in characteristic two, II

2025/03/09 by Zhang, Junwei, Chang, Xuewu, Jin, Ping +1
#20C15 #20C20 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2503.06429

Abstract

In 2007, J. P. Cossey conjectured that if G is a finite p-solvable group and φ is an irreducible Brauer character of G with vertex Q, then the number of lifts of φ is at most |Q:Q'|. In this paper we revisited Cossey's conjecture for p=2 from the perspective of Navarro vertices and obtained a new way to count the number of lifts of φ. Some applications were given.

Related

• Lifts of Brauer characters in characteristic two
• Counting lifts of irreducible Brauer characters
• Counting lifts of Brauer characters
• A construction of two distinct canonical sets of lifts of Brauer characters of a p-solvable group
• Bounds on the number of lifts of a Brauer character in a p-solvable group