Finite primitive groups of small rank: symmetric and sporadic groups

Finite primitive groups of small rank have been studied for a long time because they are a natural source of important examples and because of their applications to various parts of mathematics. This interest has brought to the classification of finite primitive groups of small rank. Historically, in this context, the word “small” means absolute constant. This paper is part of a series aiming to classify finite primitive groups of small rank, where the word “small” is not an absolute constant. We have various motivations for embarking in this classification, ranging from representation theory to combinatorics. We start our work considering almost simple groups whose socle is either an alternating or a sporadic simple group.