From mreid@ptc.com  Tue Mar  7 14:35:00 1995
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Date: Tue, 7 Mar 1995 14:49:04 -0500
From: mreid@ptc.com (michael reid)
Message-Id: <9503071949.AA26403@ducie>
To: cube-lovers@ai.mit.edu, mark.longridge@canrem.com
Subject: New GAP insights
Content-Length: 1222

for what it's worth, i'll make some conjectures about mark's questions.

> A) What is the next most commutative element (the pancentre?)
>   after the 12-flip?

(presumably, start excluded as well)

i'll guess that these four conjugacy classes are tied for next.

corner cycle structure:  (1+)(1+)(1+)(1+)(1+)(1+)(1+)(1-)
edge cycle structure:    (1)(1)(1)(1)(1)(1)(1)(1)(1)(1)(1)(1)

corner cycle structure:  (1+)(1+)(1+)(1+)(1+)(1+)(1+)(1-)
edge cycle structure:    (1+)(1+)(1+)(1+)(1+)(1+)(1+)(1+)(1+)(1+)(1+)(1+)

corner cycle structure:  (1+)(1-)(1-)(1-)(1-)(1-)(1-)(1-)
edge cycle structure:    (1)(1)(1)(1)(1)(1)(1)(1)(1)(1)(1)(1)

corner cycle structure:  (1+)(1-)(1-)(1-)(1-)(1-)(1-)(1-)
edge cycle structure:    (1+)(1+)(1+)(1+)(1+)(1+)(1+)(1+)(1+)(1+)(1+)(1+)

> B) What is the least commutative element (the anticentre?) of
>   the cube group?

i'll guess

corners:  (1)(7)     edges:    (1)(11)
corners:  (1+)(7-)   edges:    (1)(11)
corners:  (1-)(7+)   edges:    (1)(11)
corners:  (1)(7)     edges:    (1+)(11+)
corners:  (1+)(7-)   edges:    (1+)(11+)
corners:  (1-)(7+)   edges:    (1+)(11+)

each of these splits into two conjugacy classes.  i think this is the
example bandelow gives in his book.

mike