Subnormalisers of semisimple elements in finite groups of Lie type

2025/11/03 by Malle, Gunter
#20D06 #20D20 #20D35 #20E25 #20G40 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2511.01557

Abstract

We determine subnormalisers of semisimple elements of prime power order in finite quasi-simple groups of Lie type. For this, we determine the maximal overgroups of normalisers of Sylow tori. This is motivated by the recent character correspondence conjecture by Moretó and Rizo as well as by the question of existence of quasi-semiregular elements in finite permutation groups.

Citations

• The Picky Conjecture for groups of Lie type
• Finite permutation groups with quasi-semiregular elements
• Picky elements, subnormalisers, and character correspondences
• The development version of the CHEVIE package of GAP3

Cited by

• The Moretó-Rizo conjectures for symmetric groups

Related

• Picky elements, subnormalisers, and character correspondences
• On maximal embeddings of finite quasisimple groups
• Restrictions of irreducible characters of finite groups of Lie type to derived subgroups and regular semisimple elements
• Finite permutation groups with quasi-semiregular elements
• A note on the normal subgroup lattice of ultraproducts of finite\n quasisimple groups