Characters, Hall subgroups, and Normal Complements

2024/06/23 by Guralnick, Robert, Navarro, Gabriel
#20C15 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2406.16184

Abstract

If H is a Hall subgroup of a finite group G, it was proven in 1989 using the classification of finite simple groups that all the irreducible complex characters of H extend to G if and only if there is N\trianglelefteq G such that HN=G and H∩ N=1. In this note we offer a modular version of this result under more general hypothesis.

Related

• Hall complement numbers
• Frattini Argument for Hall subgroups
• Normal p-complements and irreducible character codegrees
• Clifford correspondences and irreducible restrictions of characters
• Characters of p'-degree and Thompson's character degree theorem