From boland@sci.kun.nl Thu Oct 19 21:41:58 1995
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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