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.

Muzychuk, M., Spiga, P. (2020). Finite primitive groups of small rank: symmetric and sporadic groups. JOURNAL OF ALGEBRAIC COMBINATORICS, 52(2), 103-136 [10.1007/s10801-019-00896-5].

### Finite primitive groups of small rank: symmetric and sporadic groups

#### Abstract

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.
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Multiplicity-free character; Permutation character; Primitive group; Rank; Simple group;
English
2020
103
136
34
Muzychuk, M., Spiga, P. (2020). Finite primitive groups of small rank: symmetric and sporadic groups. JOURNAL OF ALGEBRAIC COMBINATORICS, 52(2), 103-136 [10.1007/s10801-019-00896-5].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10281/345888`