Talk:Periodic group

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Mathematics rating:	Stub Class	Low Priority	Field: Algebra
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Geometry guy 16:02, 22 May 2007 (UTC)

[edit] Aren't all finite groups periodic?

OK, I might have forgotten all my maths, but aren't all finite groups periodic? (Because every element has order at most the order of the group) This would make the 2nd sentence of the 1st para ("Finite cyclic groups are examples of periodic groups.") misleading - all finite groups, cyclic or not, are periodic. —This unsigned comment was added by [[User:{{{1}}}|{{{1}}}]] ([[User talk:{{{1}}}|talk]] • [[Special:Contributions/{{{1}}}|contribs]]) .

Good point, my original edit was to try and tidy up the sentence

The concept of a periodic group should not be confused with that of a cyclic group.

which I find unsatisfactory. Somehow it seems it cyclic groups should get a mention, but I'm not sure how. --Salix alba (talk) 07:59, 28 March 2006 (UTC)

[edit] Example needed

There should be an example of periodic group which is not finite. --193.198.16.211 (talk) 21:15, 5 May 2008 (UTC)

Done. Nonabelian examples can be given in similar fashions: an infinite dimensional extraspecial group, the union of the finite symmetric groups, etc. JackSchmidt (talk) 14:03, 6 May 2008 (UTC)