[next] [prev] [up] Date: Thu, 16 Nov 95 01:33:05 +0100
[next] [prev] [up] From: Michiel Boland <boland@sci.kun.nl >
~~~ [prev] [up] Subject: Re: God's Algorithm for the 1x1x1 Rubik's Cube

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 <boland@sci.kun.nl>
University of Nijmegen
The Netherlands

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