Talk:Powerful p-group

Who was this written for?

I was poking the "Random Article" button, and this page came up. And so did some questions.

If the reader knows what this sentence means:

The Frattini subgroup Φ(G) of G has the property Φ(G) = Gp.

then that reader does not need this article. That reader is already familiar with the concept of a powerful group, and the inner workings of a Frattini subgroup are, well, child's play.

If, by contrast, one does NOT know what this sentence means:

The Frattini subgroup Φ(G) of G has the property Φ(G) = Gp.

then nothing in the article will help in the tiniest bit. A Frattini subgroup could be a collection of folks from tiny college fraternities (they're called not "frats" but "frattinis") or maybe it's a subset of Padanian anarchists loyal to their martyred leader Silvestro Frattini...

So who was this article written for?

Where did any of this come from?

Does the author know what the word "citation" means?

Timothy Perper 00:54, 1 December 2007 (UTC)

Thank you very much for the changes, including the introduction and the citations. Now the article has a place -- I'm tempted to say a "locus" -- in Wikidiscourse space, which in plain English means we know where it starts and where it goes. Without doubt, the entry will not be very lucid to a non-mathematician, but such a reader can back up on the links in the introduction, or, if they are knowledgeable, can read the more advanced treatises cited. And that -- in my opinion -- is how to handle all problems like this one: an introduction with links to more basic material and a ref list with citations to more advanced stuff.

This way (as my wife just pointed out) a "Frattini subgroup" no longer sounds like a kind of pasta or maybe, she said, an Italian pastry.

Good work. Maybe somebody could add a worked out example?

Timothy Perper 16:00, 1 December 2007 (UTC)

Citation for some less obvious results?

Every finite p-group can be expressed as a section of a powerful p-group.

So I actually have all three of the books cited, and have been slowly studying them for about 2 weeks. And essentially every other result cited on this page, I can verify, except this one. It would be good if the author could attribute it with either theorem / lemma / proposition number, or a page number, to one of the sources cited?

Sorry I didn't log in, I forgot my password. Chris [render787] —Preceding unsigned comment added by 66.27.52.186 (talk) 21:11, 25 June 2010 (UTC)

Actually, I found this result in the exercises of chapter 2, in my version the 1991 one of p-adic Analytic Groups, it is Exercise 16 of chapter 2. Chris [render787] —Preceding unsigned comment added by 132.239.90.106 (talk) 23:52, 27 June 2010 (UTC)