[r-t] re: proofs
Robin Woolley
robin at robinw.org.uk
Tue Oct 5 09:26:29 UTC 2004
Re: Graham's e-mail.
As I understand the concept of a group, any two members of the group
'combined' according to the rules of the group give a third member of the
group.
Now 'B', for example, is often referred to as a 'FCH GROUP'. Two members of
the group are 24365 and 25436. Combining them either way gives 24563 and
26345 which are members of FCH groups T and F respectively. Looking in the
literature I see that they could be defined as semi-groups, however.
As Graham says, the complete set of 720 forms a group, S6, to be precise.
(By the way, surely S for 'symmetric' refers to the fact that the origin of
this group is from the symmetries of plane figures - not because it's
symmetrical, as someone said earlier, which it quite clearly isn't - being
non-abelian.) The 360 in-course course-heads form the group A6. S6 is not a
falseness group either - it is just the complete set of possible course
heads.
This does not change the fact that what we happily call 'groups' are not in
this case - nor are they even sub-groups.
Remember this: they are referred to in this way in CC pubs - I could give
chapter & verse, but I won't.
Then again, it's more than 30 years since I first encountered the concept of
a group - so no doubt fashion has changed the definition. (Probably doesn't
need to be associative to be a group, now!!).
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