https://groupprops.subwiki.org/w/index.php?title=Fusion_system_induced_by_a_finite_group_on_its_p-Sylow_subgroup_is_functorial&feed=atom&action=historyFusion system induced by a finite group on its p-Sylow subgroup is functorial - Revision history2020-11-28T04:57:09ZRevision history for this page on the wikiMediaWiki 1.29.2https://groupprops.subwiki.org/w/index.php?title=Fusion_system_induced_by_a_finite_group_on_its_p-Sylow_subgroup_is_functorial&diff=19756&oldid=prevVipul: Created page with '==Statement== Suppose <math>p</math> is a prime number. Consider the map from the category of finite groups to the category of fusion systems that sends a finite group to th…'2009-08-01T20:42:47Z<p>Created page with '==Statement== Suppose <math>p</math> is a <a href="/wiki/Prime_number" title="Prime number">prime number</a>. Consider the map from the category of finite groups to the category of fusion systems that sends a finite group to th…'</p>
<p><b>New page</b></p><div>==Statement==<br />
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Suppose <math>p</math> is a [[prime number]]. Consider the map from the category of finite groups to the category of fusion systems that sends a finite group to the [[fact about::fusion system induced by a finite group on its p-Sylow subgroup|fusion system induced on its p-Sylow subgroup]]. This map is functorial. In particular:<br />
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* A [[homomorphism of groups]] induces a [[morphism of fusion systems]].<br />
* The morphism of fusion systems induced by the identity morphism is the identity morphism.<br />
* The morphism of fusion systems induced by a composite of two homomorphisms is the composite of the morphisms induced by each of them.</div>Vipul