https://groupprops.subwiki.org/w/index.php?action=history&feed=atom&title=Group_admitting_a_partition_into_cyclic_subgroups 2026-05-16T10:36:47Z Revision history for this page on the wiki MediaWiki 1.41.2 https://groupprops.subwiki.org/w/index.php?title=Group_admitting_a_partition_into_cyclic_subgroups&diff=24055&oldid=prev 2010-03-08T21:29:17Z

<p>Created page with &#039;{{wikilocal}} {{group property}} ==Definition== A &#039;&#039;&#039;group admitting a partition into cyclic subgroups&#039;&#039;&#039; is defined as a <a href="/wiki/Group" title="Group">group</a> that can be expressed as a union of cyclic s…&#039;</p> <p><b>New page</b></p><div>{{wikilocal}}<br /> {{group property}}<br /> <br /> ==Definition==<br /> <br /> A &#039;&#039;&#039;group admitting a partition into cyclic subgroups&#039;&#039;&#039; is defined as a [[group]] that can be expressed as a union of cyclic subgroups any two of which have trivial intersection. In other words, it admits a [[fact about::partition of a group]] where all the parts are cyclic subgroups.<br /> <br /> <br /> ==Relation with other properties==<br /> <br /> ===Stronger properties===<br /> <br /> {| class=&quot;sortable&quot; border=&quot;1&quot;<br /> ! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions<br /> |-<br /> | [[Weaker than::Cyclic group]] || || || || {{intermediate notions short|group admitting a partition into cyclic subgroups|cyclic group}}<br /> |-<br /> | [[Weaker than::Elementary abelian group]] || || || || {{intermediate notions short|group admitting a partition into cyclic subgroups|elementary abelian group}}<br /> |-<br /> | [[Weaker than::Group of prime exponent]] || || || || {{intermediate notions short|group admitting a partition into cyclic subgroups|group of prime exponent}}<br /> |-<br /> | [[Weaker than::Dihedral group]] || || || || {{intermediate notions short|group admitting a partition into cyclic subgroups|dihedral group}}<br /> |-<br /> | [[Generalized dihedral group]] for an [[elementary abelian group]] || || || ||<br /> |-<br /> | Subgroup of the affine group over a finite field || || || || <br /> |}<br /> <br /> ===Weaker properties===<br /> <br /> {| class=&quot;sortable&quot; border=&quot;1&quot;<br /> ! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions<br /> |-<br /> | [[Stronger than::Group admitting a partition into abelian subgroups]] || || || ||<br /> |}</div>

Vipul