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The Maximal Subgroups of the Low-Dimensional Finite Classical Groups by Colva M. Roney-Dougal, Derek F. Holt, John N. Bray

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1Introduction

1.1 Background

Given a group G, we write Soc G for the socle of G: the subgroup of G generated by its minimal normal subgroups. A group G is almost simple if image for some non-abelian simple group S. Note that S = Soc G. A group G is perfect if G = G′. A group G is quasisimple if G is perfect and G/Z(G) is a non-abelian simple group.

Aschbacher [1] proves a classification theorem, which subdivides the subgroups of the finite classical groups into nine classes. The first eight of these consist roughly of groups that preserve some kind of geometric structure; for example the first class, , consists (roughly) of the reducible groups, which ...

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