“The second maximal subgroups of the almost simple groups”
Lunedi 12 Maggio 2025, ore 14:30 - Aula 2AB40 - Patricia Medina Capilla (Università di Warwick)
Abstract
In 2018, Lucchini, Marion, and Tracey showed that every maximal subgroup of an almost simple group is 5-generated, lowering the previously known bound of 6. Naturally, one can ask the same about second maximal subgroups of almost simple groups. Burness, Liebeck and Shalev looked into this question in 2016, determining that almost all such subgroups were 70-generated. In this talk, we will present recent work aiming to lower this bound, and survey some of the key techniques involved. In particular, we will discuss the method of crowns, developed by Lucchini and Dalla Volta and used by Lucchini, Marion and Tracey to great effect, as well as an improved classification of the second maximal subgroups of almost simple groups with alternating or classical socle. Finally, we will see some of the interesting representation-theoretic problems which arise when classifying such second maximal subgroups.
