[r-t] Re: Proofs

R.P.I. Lewis mapc01 at bangor.ac.uk
Tue Sep 28 11:12:32 UTC 2004

> I'm beginning to wish I hadn't got along with Philip's suggestion.

Sorry, I was just making a suggestion (I would not have mentioned it but I
did not understand the last part of what you wrote, and I thought while i
was asking what it meant I'd add it in, in case someone was interested..)
I did not realise it would upset you!

> X(AC) here means just the falseness between A & C - no 'direction' is
> intended but having decided on the rule 'inverse of second of the pair
> operating on the first of the pair', we're stuck with it.

if there was really no direction then why do we not get X(AC)=X(CA)? Seems
to me that the fact that X is not symmetric tells us something

> My wife, who, to save her from ennui, is currently doing
> an M.Math course at the Open U (M336) confirms my recollection from 30 years
> ago that the convention (then and now) is that 'ab' is 'a operating on b'
> or, if you like as I say sotto voce when I write it down, 'a of b'.

It rerally depends on what "operating on" means.  there are left
operations and right operations, and a group operates on itself by both
left multiplication and right multiplication.  Actually left and right
actions are a separate issue to the convention for how you write group

> In fact, the whole analysis is just as valid the other way round, C.inv(A),
> except that it might be less natural when starting from first principles.
> The definition of J in words is the permutation  for a seconds place lead

as in "J=12"? Is this a standard notation, and if so where should I have
looked to find this out for myself?

> end so:
> > e = rpJ => rp = J
> >
> >Here you meant to type "e = rpJ => pr = J" I suppose
> No! - since J is self-inverse, it makes no difference: J = pr = rp.

Oh OK, I did not realise that J was a place notation.

> Anyway, I said in the pre-amble:
> "An asymmetric section may also have just one falseness group."
> Inspection of the appropriate collection will show that it is usual for any
> asymmetric section to lead to  two distinct falseness groups.

ah... when you say "falseness groups" you don't mean a group in the
mathematical sense, you just meant letters? sorry, this confused me... I
*thought* that what you were doing was to take the values of X and
generate a subgroup, (which would hopefully tell us something about the

Just goes to show that people who talk maths don't have the monopoly on
confusing people with undefined terms...

More information about the ringing-theory mailing list