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• CommentRowNumber1.
• CommentAuthorMike Shulman
• CommentTimeJun 26th 2014

I added a bunch of material to nilpotent group, including an inductive definition of nilpotency and of central series (which is how proofs about nilpotent groups often actually go) and a mention of the dual coinductive notions.

• CommentRowNumber2.
• CommentAuthorDavid_Corfield
• CommentTimeJun 26th 2014

’Upper central series’ at nilpotent group links back to the page it’s on. What’s its definition?

Could you have an entity with central streams which don’t bottom out, i.e., keep giving nontrivial quotients?

• CommentRowNumber3.
• CommentAuthorMike Shulman
• CommentTimeJun 26th 2014

For the first question, you could try wikipedia. For the second, I don’t see why not, though of course you’d need an infinite group to start with; but I’m not a group theorist.

• CommentRowNumber4.
• CommentAuthorTodd_Trimble
• CommentTimeJun 26th 2014

I didn’t understand why “upper central series” called on the page again (it should have produced a gray link). As a patch I added a pointer to Wikipedia.

• CommentRowNumber5.
• CommentAuthorDavid_Corfield
• CommentTimeJun 27th 2014

To remind myself for later, information here.

• CommentRowNumber6.
• CommentAuthorTobyBartels
• CommentTimeJun 27th 2014
• (edited Jun 27th 2014)

I removed redirects so that upper central series no longer redirects to nilpotent group.

Does anybody know what the attempted redirect from characteristic series was supposed to be about?

• CommentRowNumber7.
• CommentAuthorMike Shulman
• CommentTimeJun 27th 2014

Perhaps a mistake because http://en.wikipedia.org/wiki/Central_series says

The lower central series and upper central series (also called the descending central series and ascending central series, respectively), are characteristic series, which, despite the names, are central series if and only if a group is nilpotent.

• CommentRowNumber8.
• CommentAuthorDavid_Corfield
• CommentTimeJun 27th 2014

I put in some content at upper central series.

• CommentRowNumber9.
• CommentAuthorTim_Porter
• CommentTimeJun 27th 2014
• (edited Jun 27th 2014)

I have added a bit to characteristic series and created a stub on subgroup series.

• CommentRowNumber10.
• CommentAuthorDavid_Corfield
• CommentTimeSep 26th 2018

Every finite nilpotent group, $G$, is the direct product of its Sylow subgroups, each of which is a normal subgroup of $G$.

• CommentRowNumber11.
• CommentAuthorGuest
• CommentTimeApr 24th 2020
In the “expand out” paragraph in the third exact sequence this needs to be a G/G_3 at the end (not G/G_2).
• CommentRowNumber12.
• CommentAuthorTodd_Trimble
• CommentTimeApr 24th 2020

Took care of it.