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Wednesday, November 18, 2020

Qube Problem

Filed under: General — Tags: — m759 @ 9:42 PM

See today’s update to my November 11 post Qube.

Wednesday, November 11, 2020

Qube

Filed under: General — Tags: — m759 @ 8:30 PM

The new domain qube.link  forwards to . . .
http://finitegeometry.org/sc/64/solcube.html .

More generally, qubes.link  forwards to this post,
which defines qubes .

Definition: A qube  is a positive integer that is
a prime-power cube , i.e. a cube that is the order
of a Galois field. (Galois-field orders in general are
customarily denoted by the letter q .)

Examples:  8, 27, 64.  See qubes.site.

Update on Nov. 18, 2020, at about 9:40 PM ET —

Problem:

For which qubes, visualized as n×n×n arrays,
is it it true that the actions of the two-dimensional
galois-geometry affine group on each n×n face, extended
throughout the whole array, generate the affine group
on the whole array? (For the cases 8 and 64, see Binary
Coordinate Systems and  Affine Groups on Small
Binary Spaces.)

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