Litterick, AJ (2018) 'On nongeneric finite subgroups of exceptional algebraic groups.' Memoirs of the American Mathematical Society, 253 (1207). 1  168. ISSN 00659266

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Abstract
© 2018 American Mathematical Society. The study of finite subgroups of a simple algebraic group G reduces in a sense to those which are almost simple. If an almost simple subgroup of G has a socle which is not isomorphic to a group of Lie type in the underlying characteristic of G, then the subgroup is called nongeneric. This paper considers nongeneric subgroups of simple algebraic groups of exceptional type in arbitrary characteristic. A finite subgroup is called Lie primitive if it lies in no proper subgroup of positive dimension. We prove here that many nongeneric subgroup types, including the alternating and symmetric groups Altn, Symn for n ≥ 10, do not occur as Lie primitive subgroups of an exceptional algebraic group. A subgroup of G is called Gcompletely reducible if, whenever it lies in a parabolic subgroup of G, it lies in a conjugate of the corresponding Levi factor. Here, we derive a fairly short list of possible isomorphism types of nonGcompletely reducible, nongeneric simple subgroups. As an intermediate result, for each simply connected G of exceptional type, and each nongeneric finite simple group H which embeds into G/Z(G), we derive a set of feasible characters, which restrict the possible composition factors of V ↓ S, whenever S is a subgroup of G with image H in G/Z(G), and V is either the Lie algebra of G or a nontrivial Weyl module for G of least dimension. This has implications for the subgroup structure of the finite groups of exceptional Lie type. For instance, we show that for n ≥ 10, Altn and Symn, as well as numerous other almost simple groups, cannot occur as a maximal subgroup of an almost simple group whose socle is a finite simple group of exceptional Lie type.
Item Type:  Article 

Divisions:  Faculty of Science and Health > Mathematical Sciences, Department of 
Depositing User:  Elements 
Date Deposited:  05 Sep 2019 10:25 
Last Modified:  27 Sep 2019 13:15 
URI:  http://repository.essex.ac.uk/id/eprint/25253 
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