Classification of finite simple groups: Difference between revisions
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imported>ALittleClass →Consequences of the classification: added mention of graph isomorphism problem |
imported>MathsHistorian →Consequences of the classification: Add another application -- characterization by commuting graphs |
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|style="vertical-align:top"|2012 | |style="vertical-align:top"|2012 | ||
|Gonthier and collaborators announce a computer-checked version of the [[Feit–Thompson theorem]] using the [[Coq | |Gonthier and collaborators announce a computer-checked version of the [[Feit–Thompson theorem]] using the [[Rocq]] (then: ''Coq'') [[proof assistant]].<ref>{{cite web |url=http://www.msr-inria.fr/news/feit-thomson-proved-in-coq/ |title=Feit–Thompson theorem has been totally checked in Coq |publisher=Msr-inria.inria.fr |date=2012-09-20 |access-date=2012-09-25 |archive-url=https://web.archive.org/web/20161119094854/http://www.msr-inria.fr/news/feit-thomson-proved-in-coq/ |archive-date=2016-11-19 |url-status=dead }}</ref> | ||
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This section lists some results that have been proved using the classification of finite simple groups. | 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:// | *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://dx.doi.org/10.1016/0022-0000%2882%2990009-5 |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|url-access=subscription }}</ref> | ||
*The [[Schreier conjecture]] | *The [[Schreier conjecture]] | ||
*The [[Signalizer functor theorem]] | *The [[Signalizer functor theorem]] | ||
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*The [[Sims conjecture]]<ref>{{cite journal|last1=Cameron |first1=P. J. |last2=Praeger |first2=C. E. |last3=Saxl |first3=J. |last4=Seitz |first4=G. M. |author-link1=Peter Cameron (mathematician) |author-link2=Cheryl Praeger |author-link3=Jan Saxl|author-link4=Gary Seitz |title=On the Sims conjecture and distance transitive graphs |journal=[[Bull. London Math. Soc.]] |volume=15 |year=1983 |issue=5 |pages=499–506 |doi=10.1112/blms/15.5.499}}</ref> | *The [[Sims conjecture]]<ref>{{cite journal|last1=Cameron |first1=P. J. |last2=Praeger |first2=C. E. |last3=Saxl |first3=J. |last4=Seitz |first4=G. M. |author-link1=Peter Cameron (mathematician) |author-link2=Cheryl Praeger |author-link3=Jan Saxl|author-link4=Gary Seitz |title=On the Sims conjecture and distance transitive graphs |journal=[[Bull. London Math. Soc.]] |volume=15 |year=1983 |issue=5 |pages=499–506 |doi=10.1112/blms/15.5.499}}</ref> | ||
*[[Frobenius's theorem (group theory)|Frobenius's conjecture]] on the number of solutions of {{nowrap|1=''x''<sup>''n''</sup> = 1}}. | *[[Frobenius's theorem (group theory)|Frobenius's conjecture]] on the number of solutions of {{nowrap|1=''x''<sup>''n''</sup> = 1}}. | ||
* Non-abelian finite simple groups are characterized by their [[commuting graph|commuting graphs]].<ref>{{cite journal |last1=Solomon |first1=Ronald M. |last2=Woldar |first2=Andrew J. |title=Simple groups are characterized by their non-commuting graphs |journal=Journal of Group Theory |date=1 November 2013 |volume=16 |issue=6 |pages=793–824 |doi=10.1515/jgt-2013-0021}}</ref> | |||
==See also== | ==See also== | ||