From:

~~~ Subject:

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 <boland@sci.kun.nl>

University of Nijmegen

The Netherlands