https://wiki.tachyony.co.uk/w/index.php?action=history&feed=atom&title=Classification_of_finite_simple_groups 2026-06-16T22:44:55Z Revision history for this page on the wiki MediaWiki 1.44.0 https://wiki.tachyony.co.uk/w/index.php?title=Classification_of_finite_simple_groups&diff=67046&oldid=prev 2025-11-16T18:51:40Z

<p><span class="autocomment">Consequences of the classification: </span> Add another application -- characterization by commuting graphs</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 19:51, 16 November 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l321">Line 321:</td> <td colspan="2" class="diff-lineno">Line 321:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|style=&quot;vertical-align:top&quot;|2012</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|style=&quot;vertical-align:top&quot;|2012</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>|Gonthier and collaborators announce a computer-checked version of the [[Feit–Thompson theorem]] using the [[Coq <del style="font-weight: bold; text-decoration: none;">(software</del>)<del style="font-weight: bold; text-decoration: none;">|Coq]] </del>[[proof assistant]].&lt;ref&gt;{{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 }}&lt;/ref&gt;</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>|Gonthier and collaborators announce a computer-checked version of the [[Feit–Thompson theorem]] using the [[<ins style="font-weight: bold; text-decoration: none;">Rocq]] (then: ''</ins>Coq<ins style="font-weight: bold; text-decoration: none;">''</ins>) [[proof assistant]].&lt;ref&gt;{{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 }}&lt;/ref&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l347">Line 347:</td> <td colspan="2" class="diff-lineno">Line 347:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>This section lists some results that have been proved using the classification of finite simple groups.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>This section lists some results that have been proved using the classification of finite simple groups.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*A breakthrough in the best known theoretical algorithm for the [[graph isomorphism problem]] in 1982&lt;ref&gt;{{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://<del style="font-weight: bold; text-decoration: none;">www</del>.<del style="font-weight: bold; text-decoration: none;">sciencedirect</del>.<del style="font-weight: bold; text-decoration: none;">com</del>/<del style="font-weight: bold; text-decoration: none;">science</del>/<del style="font-weight: bold; text-decoration: none;">article/pii/0022000082900095 </del>|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}}&lt;/ref&gt;</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*A breakthrough in the best known theoretical algorithm for the [[graph isomorphism problem]] in 1982&lt;ref&gt;{{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://<ins style="font-weight: bold; text-decoration: none;">dx</ins>.<ins style="font-weight: bold; text-decoration: none;">doi</ins>.<ins style="font-weight: bold; text-decoration: none;">org</ins>/<ins style="font-weight: bold; text-decoration: none;">10.1016</ins>/<ins style="font-weight: bold; text-decoration: none;">0022-0000%2882%2990009-5 </ins>|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<ins style="font-weight: bold; text-decoration: none;">|url-access=subscription </ins>}}&lt;/ref&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*The [[Schreier conjecture]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*The [[Schreier conjecture]]</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*The [[Signalizer functor theorem]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*The [[Signalizer functor theorem]]</div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l357">Line 357:</td> <td colspan="2" class="diff-lineno">Line 357:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*The [[Sims conjecture]]&lt;ref&gt;{{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}}&lt;/ref&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*The [[Sims conjecture]]&lt;ref&gt;{{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}}&lt;/ref&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*[[Frobenius&#039;s theorem (group theory)|Frobenius&#039;s conjecture]] on the number of solutions of {{nowrap|1=&#039;&#039;x&#039;&#039;&lt;sup&gt;&#039;&#039;n&#039;&#039;&lt;/sup&gt; = 1}}.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*[[Frobenius&#039;s theorem (group theory)|Frobenius&#039;s conjecture]] on the number of solutions of {{nowrap|1=&#039;&#039;x&#039;&#039;&lt;sup&gt;&#039;&#039;n&#039;&#039;&lt;/sup&gt; = 1}}.</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* Non-abelian finite simple groups are characterized by their [[commuting graph|commuting graphs]].&lt;ref&gt;{{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}}&lt;/ref&gt;</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==See also==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==See also==</div></td></tr> </table>

imported>MathsHistorian https://wiki.tachyony.co.uk/w/index.php?title=Classification_of_finite_simple_groups&diff=16957&oldid=prev 2025-06-25T21:20:34Z

<p><span class="autocomment">Consequences of the classification: </span> added mention of graph isomorphism problem</p> <a href="https://wiki.tachyony.co.uk/w/index.php?title=Classification_of_finite_simple_groups&amp;diff=16957">Show changes</a>

imported>ALittleClass