Took care of it.

]]>Added the sentence:

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

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

]]>I put in some content at upper central series.

]]>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.

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?

]]>To remind myself for later, information here.

]]>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.

]]>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.

]]>’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?

]]>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.

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