From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/28 Path: news.gmane.org!not-for-mail From: "Ronnie Brown" Newsgroups: gmane.science.mathematics.categories Subject: It it a good idea to use the term 2-group outside of its use in group thoery? Date: Fri, 30 Jan 2009 23:34:26 -0000 Message-ID: Reply-To: "Ronnie Brown" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1233411425 22399 80.91.229.12 (31 Jan 2009 14:17:05 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sat, 31 Jan 2009 14:17:05 +0000 (UTC) To: "categories" Original-X-From: categories@mta.ca Sat Jan 31 15:18:15 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 1LTGfj-0006rF-6n for gsmc-categories@m.gmane.org; Sat, 31 Jan 2009 15:18:11 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LTG3y-0006AQ-CE for categories-list@mta.ca; Sat, 31 Jan 2009 09:39:10 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:28 Archived-At: 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:=20 "In mathematics, given a prime number p, a p-group is a periodic group = in which each element has a power of p as its order. That is, for each = element g of the group, there exists a nonnegative integer n such that g = to the power pn is equal to the identity element. Such groups are also = called primary."=20 I feel we should try to avoid and even to reduce confusion, = especially as there are claims that crossed modules, for example, can be = thought of as `2-dimensional groups' (I agree with this, of course!); = there are nice crossed modules M \to P in which M and P are 2-groups in = the group theoretic sense!=20 My favourite example is=20 \mu: Z_2 \times Z_2 \to Z_4=20 in which Z_4 acts by the twist (of order 2), and \mu maps each factor = Z_2 injectively into Z_4. This crossed module has non trivial = k-invariant. I think Johannes Huebschmann first observed this.=20 So an example oriented approach to crossed modules could well need the = term p-group in its standard group theoretic usage. Some examples of = finite crossed modules are in=20 R. Brown and C.D. Wensley, `Computation and homotopical applications of induced crossed modules', J. Symbolic Computation 35 (2003) 59-72. However I think one can be happy with the well established term = 2-groupoid.=20 I would just like this point to be discussed: terminology is important, = and confusing an established use might raise hackles unnecessarily.=20 Ronnie