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This section lists some results that have been proved using the classification of finite simple groups.
*A breakthrough in the best known theoretical algorithm for the [[graph isomorphism problem]] in 1982<ref>{{Cite journal |last=Luks |first=Eugene M. |date=1982-08-01 |title=Isomorphism of graphs of bounded valence can be tested in polynomial time |url=https://www.sciencedirect.com/science/article/pii/0022000082900095 |journal=Journal of Computer and System Sciences |volume=25 |issue=1 |pages=42–65 |doi=10.1016/0022-0000(82)90009-5 |issn=0022-0000}}</ref>
*The [[Schreier conjecture]]
*The [[Signalizer functor theorem]]
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