The classification of finite simple groups, whether it be viewed as finished, or as a work in progress, is (or will be) without doubt an enormous achievement. It clearly sheds a great deal of light on the structure of finite groups. However, as with the classification of simple Lie algebras, one might expect this to have a significant impact outside of the immediate subject. So what are some of the known, or expected, applications to the classification outside of finite group theory?

NB:

this question was significantly edited by other users soon after being posted (Aug 2 '10). The few critical comments below were actually addressed before the question was edited and improved.

To anyone who has doubts about the proof, please see Aschbacher's

*Notices*paper "The status of the classification of the finite simple groups" and please rather don't debate that particular matter here.

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