From:

~~~ Subject:

Martin Schoenert states:

Only one out of 332640 elements of GE (and of G) centralizes P.

That is to say that the index of the centralizer of P in GE has index

332640 in GE. Since all elements of GC commute with all elements of

GE, the index of the centralizer of P in G also has index 332640 in G.

Z is indeed the center of GE', GE, G, G', and GCE.

I get the fact that only the super-flip (or 12-flip) is the centre of

G and the centre of GE. Another way to look at it would be the centre

of the cube group must effect all the corners & edges in the same

way, and only the super-flip fits these conditions when we allow

all 6 generators < U, D, F, B, L, R > to be used.

In the case of the smaller group < U, R > we can get 6 corners twisted

either clockwise or counter-clockwise, thus effecting all the corners

and edges the same, due to the fact we can have 6 twists the same and

< U, R > only contains 6 corners, and so this is the centre of

< U, R >.

But I don't understand how only one out of 332,640 elements of GE

and G centralizes P. I thought that GE had:

(12 ^ 2 / 2 ) * 12! = 980,995,276,800 elements

That is to say that the group on the cube of edges only has

980,995,276,800 elements. To be honest I'm not sure what P

represents! Jerry refers to P as the Pons Asinorum, but I think

the term may have two meanings in the two messages.

Z is the centre of G right? I need an ANSI standard math dictionary,

but I doubt such a book exists.

I'm going to tackle some more cube terminology in my next message.

-> Mark <-

Email: mark.longridge@canrem.com