https://groupprops.subwiki.org/w/index.php?action=history&feed=atom&title=Homocyclic_normal_subgroup 2026-11-03T12:42:46Z Revision history for this page on the wiki MediaWiki 1.41.2 https://groupprops.subwiki.org/w/index.php?title=Homocyclic_normal_subgroup&diff=22200&oldid=prev 2009-10-19T22:01:11Z

<p>Created page with &#039;{{group-subgroup property conjunction|normal subgroup|homocyclic group}} ==Definition== A <a href="/wiki/Subgroup" title="Subgroup">subgroup</a> of a <a href="/wiki/Group" title="Group">group</a> is termed a &#039;&#039;&#039;homocyclic normal subgroup&#039;&#039;&#039; if it is a [[…&#039;</p> <p><b>New page</b></p><div>{{group-subgroup property conjunction|normal subgroup|homocyclic group}}<br /> <br /> ==Definition==<br /> <br /> A [[subgroup]] of a [[group]] is termed a &#039;&#039;&#039;homocyclic normal subgroup&#039;&#039;&#039; if it is a [[normal subgroup]] of the whole group and is also a [[homocyclic group]] as an abstract group. In other words, it is a direct product of pairwise isomorphic [[cyclic group]]s.<br /> <br /> ==Relation with other properties==<br /> <br /> ===Stronger properties===<br /> <br /> * [[Weaker than::Cyclic normal subgroup]]<br /> * [[Weaker than::Cyclic normal subgroup of finite group]]<br /> * [[Weaker than::Homocyclic normal subgroup of finite group]]<br /> <br /> ===Weaker properties===<br /> <br /> * [[Stronger than::Abelian normal subgroup]]<br /> * [[Stronger than::Class two normal subgroup]]<br /> * [[Stronger than::Nilpotent normal subgroup]]</div>

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