From boland@sci.kun.nl Thu Oct 19 21:41:58 1995 Return-Path: Received: from wn1.sci.kun.nl by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA25492; Thu, 19 Oct 95 21:41:58 EDT Received: from canteclaer.sci.kun.nl by wn1.sci.kun.nl via canteclaer.sci.kun.nl [131.174.132.34] with SMTP id CAA03659 (8.6.10/2.14) for ; Fri, 20 Oct 1995 02:41:58 +0100 Message-Id: <199510200141.CAA03659@wn1.sci.kun.nl> To: cube-lovers@ai.mit.edu Subject: Embedding G in a symmetrical group Date: Fri, 20 Oct 95 02:41:55 +0100 From: Michiel Boland It is clear that the group G of the cube (the one with 4.3252x10^19 elements) can be embedded in a symmetrical group, e.g. S_48, since each move of the cube can be seen as a permutation of 48 objects. Hence, there is a smallest number n such that G can be embedded in S_n. I'm curious to find out what this number is. It can be shown with some counting arguments that n>=32 (I'm happy to write these down but it's nicer if you thought about this first). I would be surprised if n=32 but you never know. -- Michiel Boland University of Nijmegen The Netherlands