Large orbits of Hall subgroups of solvable linear groups

2025/10/26 by Das, Samarth, Yang, Yong
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2510.22474

Abstract

Suppose that G is a finite solvable group and let H be a Hall π-subgroup, let b(H) be the largest character degree of H, we show that |G:O_{π' π}(G)|_π ≤ b(H)².

Citations

• Classifying Primitive Solvable Permutation Groups of Rank 5 and 6
• Regular orbits of finite primitive solvable groups, III

Related

• Bounding an index by the largest character degree of a solvable group
• Orbits of finite solvable groups on characters
• On The Largest Character Degree And Solvable Subgroups Of Finite Groups
• On a conjecture of Gluck
• A Criterion for the Existence of a Solvable π-Hall Subgroup in a Finite Group