From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/31 Path: news.gmane.org!not-for-mail From: Toby Bartels Newsgroups: gmane.science.mathematics.categories Subject: Re: It it a good idea to use the term 2-group outside of its use in group thoery? Date: Sat, 31 Jan 2009 11:32:53 -0800 Message-ID: Reply-To: Toby Bartels NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: ger.gmane.org 1233500378 18162 80.91.229.12 (1 Feb 2009 14:59:38 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sun, 1 Feb 2009 14:59:38 +0000 (UTC) To: categories Original-X-From: categories@mta.ca Sun Feb 01 16:00:52 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1LTdoX-0007az-HO for gsmc-categories@m.gmane.org; Sun, 01 Feb 2009 16:00:49 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LTdHV-00059N-5B for categories-list@mta.ca; Sun, 01 Feb 2009 10:26:41 -0400 Content-Disposition: inline Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:31 Archived-At: Ronnie Brown wrote: >I would like to raise an objection to using the term `2-group' as on nlab and elsehere since for the group theorists this has a specialised meaning: See the following wiki entry, especially the first 2 words: >"In mathematics, given a prime number p, a p-group is [...]" That the first 2 words are "In mathematics" rather than "In group theory, a branch of mathematics," means nothing. It's not like the Wikipedians had a discussion about it and determined that p-groups appear throughout mathematics. You do raise a good point, though. The term '2-group' is a special case of both 'p-group' and 'n-group', and these mean very different things. I wouldn't want to give up 'n-group', so I find '2-group' appropriate when (as on the n-Category Lab) one is discussing n-groups as well. But in your example about the structure of finite crossed modules, one can simply say 'crossed module', making a note that some literature calls a crossed module a '2-group' (or even 'strict 2-group'). >"[...] Such groups are also called primary." >there are claims that crossed modules, for example, can be thought of as `2-dimensional groups' In extreme cases, these show the way: both 'p-group' and 'n-group' are abbreviations, for 'p-primary group' and 'n-dimensional higher group'. So one can always use the full name or specify which usage one's paper follows. --Toby