From boland@sci.kun.nl Wed Nov 15 19:34:28 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 AA16127; Wed, 15 Nov 95 19:34:28 EST Received: from canteclaer.sci.kun.nl by wn1.sci.kun.nl via canteclaer.sci.kun.nl [131.174.132.34] with SMTP id BAA05998 (8.6.10/2.14); Thu, 16 Nov 1995 01:33:07 +0100 Message-Id: <199511160033.BAA05998@wn1.sci.kun.nl> To: Jerry Bryan Cc: Cube-Lovers Subject: Re: God's Algorithm for the 1x1x1 Rubik's Cube In-Reply-To: Your message of "Tue, 14 Nov 95 09:13:41 -0400." Date: Thu, 16 Nov 95 01:33:05 +0100 From: Michiel Boland Jerry wrote: >But can we generate C with only one generator? The >answer is no. (Proof: Order(i)=1, Order(t)=4, Order(tt)=2, Order(tf)=3, >and Order(ttf)=2. All the orders are less than 24. Note that it suffices >to calculate the order for one representative of each conjugacy class.) Another way to see that C cannot be generated by one generator is to note that C is not abelian. Singmaster mentions in his Notes that the cube group G itself can also be generated by two elements. -- Michiel Boland University of Nijmegen The Netherlands