To me, the new URL "Songlines.space" suggests both the Outback
and the University of Western Australia. For the former, see
"'Max Barry' + Lexicon" in this journal. For the latter, see SymOmega.
The new URL forwards to a combination of these posts.
Conwell, 1910 —
(In modern notation, Conwell is showing that the complete
projective group of collineations and dualities of the finite
3-space PG (3,2) is of order 8 factorial, i.e. "8!" —
In other words, that any permutation of eight things may be
regarded as a geometric transformation of PG (3,2).)
Later discussion of this same "Klein correspondence"
between Conwell's 3-space and 5-space . . .
A somewhat simpler toy model —
Related fiction — "The Bulk Beings" of the film "Interstellar."
See the previous post, "Space," as well as…
SymOmega in this journal and a suggested motto
for The University of Western Australia.
"Bobbies on bicycles two by two…" — Roger Miller, 1965
A mathematics weblog in Australia today—
Clearly, the full symmetric group contains elements
with no regular cycles, but what about other groups?
Siemons and Zalesskii showed that for any group G
between PSL(n,q) and PGL(n,q) other than for
(n,q)=(2,2) or (2,3), then in any action of G, every
element of G has a regular cycle, except G=PSL(4,2)
acting on 8 points. The exceptions are due to
isomorphisms with the symmetric or alternating groups.
(Continued from June 2, 2013)
John Bamberg continues his previous post on this subject.
See the Klein correspondence at SymOmega today and in this journal.
"The casual passerby may wonder about the name SymOmega.
This comes from the notation Sym(Ω) referring to the symmetric group
of all permutations of a set Ω, which is something all of us have
both written and read many times over."
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