[r-t] Proofs, etc

[Graham John]

Richard Smith wrote:

 
> Imagine one of the B false course heads -- say, 13245678.
> Now transpose this by another B false course head -- perhaps
> 12365478.  We end up with 13265478, which is an F false
> course head.  This means that the B falseness "group" is not
> closed and so is not, mathematically, a group.

OK - So the mathematical definition is a group closed by transposition of
other members of the same group. 

But in that case FCHs are closed transpositions at one remove, or inter-group
relationships i.e. they are mutual transpositions of a closed group (namely
the 7 leadheads of a plain course). If you transpose any leadhead of the plain
course by any leadhead of a false course, you always get a leadhead of another
false course of the same group.

14263857 (member of the plain course)
X
17856324 (member of FCH 143256)
=
15738246 (member of FCH 123654)

Graham