Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
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.
’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?
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.
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.
To remind myself for later, information here.
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?
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 put in some content at upper central series.
I have added a bit to characteristic series and created a stub on subgroup series.
Added the sentence:
Every finite nilpotent group, $G$, is the direct product of its Sylow subgroups, each of which is a normal subgroup of $G$.
Took care of it.
1 to 12 of 12