https://groupprops.subwiki.org/w/index.php?action=history&feed=atom&title=Elementarily_equivalent_groupsElementarily equivalent groups - Revision history2026-06-27T05:53:27ZRevision history for this page on the wikiMediaWiki 1.41.2https://groupprops.subwiki.org/w/index.php?title=Elementarily_equivalent_groups&diff=20337&oldid=prevVipul: Created page with '==Definition== Two groups <math>G</math> and <math>H</math> are termed '''elementarily equivalent''' if the following equivalent conditions are satisfied: * Any first-order sen…'2009-08-15T19:48:24Z<p>Created page with '==Definition== Two groups <math>G</math> and <math>H</math> are termed '''elementarily equivalent''' if the following equivalent conditions are satisfied: * Any first-order sen…'</p>
<p><b>New page</b></p><div>==Definition==<br />
<br />
Two groups <math>G</math> and <math>H</math> are termed '''elementarily equivalent''' if the following equivalent conditions are satisfied:<br />
<br />
* Any first-order sentence in the theory of groups satisfied by <math>G</math> is also satisfied for <math>H</math>, and vice versa.<br />
* There is an elementary local isomorphism between <math>G</math> and <math>H</math>.</div>Vipul