source file: mills2.txt Date: Fri, 13 Dec 1996 13:04:53 -0800 Subject: Re: definition of a group From: John Starrett >From Eric's Treasure Trove of Mathematics (on line mathematical encyclopedia) A group G is defined as a set of finite or infinite objects or operators (called ``elements'') that may be combined or ``multiplied'' to form well-defined products which satisfy 1. If A and B are two elements, then the product AB is also a member of the set. 2. The defined multiplication is associative, i.e. (AB)C A(BC) 3. There is a unit ``identity'' element I (a.k.a., 1 or E, the latter deriving from the German ``Einheit'' meaning unity) such that IA AI A for every element in the set. 4. Therex must be an inverse or reciprocal of each element. Eric's Treasure Trove http://www.gps.caltech.edu/~eww/math/math.html John Starrett Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 13 Dec 1996 23:59 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA03859; Sat, 14 Dec 1996 00:02:05 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA03855 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id PAA20689; Fri, 13 Dec 1996 15:02:03 -0800 Date: Fri, 13 Dec 1996 15:02:03 -0800 Message-Id: <3.0.32.19961213145533.00687ed0@adnc.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu