What do we know about the soluble subgroups of finite classical simple groups (and maybe their automorphism groups)? For example, are their maximal soluble subgroups explicitly known?
Soluble subgroups of finite classical simple groups
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group-theory
finite-groups
simple-groups
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0There are nontrivial bounds for soluble subgroups of $GL(n,q)$. See for example A. Mann's paper "Soluble subgroups of symmetric and linear groups" and its references. In this paper, the author said a joint paper with Z. Arad and Y. Segev about the maximal order of soluble subgroups of simple groups is in preparation, but I don't know whether such a papaer is published. – 2012-11-20