https://galois.subwiki.org/w/index.php?action=history&feed=atom&title=Absolute_Galois_groupAbsolute Galois group - Revision history2026-05-29T23:36:19ZRevision history for this page on the wikiMediaWiki 1.41.2https://galois.subwiki.org/w/index.php?title=Absolute_Galois_group&diff=75&oldid=prevVipul: Created page with '==Definition== The '''absolute Galois group''' of a field <math>K</math> is defined as the group <math>\operatorname{Aut}(\overline{K}/K)</math> where <math>\overline{K}</ma...'2009-05-14T23:21:07Z<p>Created page with '==Definition== The '''absolute Galois group''' of a <a href="/w/index.php?title=Field&action=edit&redlink=1" class="new" title="Field (page does not exist)">field</a> <math>K</math> is defined as the group <math>\operatorname{Aut}(\overline{K}/K)</math> where <math>\overline{K}</ma...'</p>
<p><b>New page</b></p><div>==Definition==<br />
<br />
The '''absolute Galois group''' of a [[field]] <math>K</math> is defined as the group <math>\operatorname{Aut}(\overline{K}/K)</math> where <math>\overline{K}</math> denotes the [[separable closure]] of <math>K</math>.<br />
<br />
The group is not just an abstract group but comes with the structure of a [[profinite group]]: it is the inverse limit of the automorphism groups for all finite Galois extensions. This also endows it with a topology (the Krull topology).</div>Vipul