https://groupprops.subwiki.org/w/index.php?title=Characteristic_rank_one_implies_cyclic-center&feed=atom&action=historyCharacteristic rank one implies cyclic-center - Revision history2019-10-15T19:12:12ZRevision history for this page on the wikiMediaWiki 1.29.2https://groupprops.subwiki.org/w/index.php?title=Characteristic_rank_one_implies_cyclic-center&diff=11460&oldid=prevVipul: New page: ==Statement== ===Property-theoretic statement=== The group property of being a finite p-group of characteristic rank one is stronger than the group property of being a [[cyclic-c...2008-07-13T20:17:39Z<p>New page: ==Statement== ===Property-theoretic statement=== The <a href="/wiki/Group_property" title="Group property">group property</a> of being a <a href="/wiki/Finite_p-group_of_characteristic_rank_one" title="Finite p-group of characteristic rank one">finite p-group of characteristic rank one</a> is stronger than the group property of being a [[cyclic-c...</p>
<p><b>New page</b></p><div>==Statement==<br />
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===Property-theoretic statement===<br />
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The [[group property]] of being a [[finite p-group of characteristic rank one]] is stronger than the group property of being a [[cyclic-center group]].<br />
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===Verbal statement===<br />
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If a [[group of prime power order]] has characteristic rank one, then its [[center]] is a [[cyclic group]].<br />
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==Proof==<br />
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This is a direct application of the fact that the center of a group is an [[Abelian characteristic subgroup]].</div>Vipul