The Sixth Meeting of the
ORESME Reading Group
January 26-27, 2001
Xavier University
In attendance:
Chris Christensen, Northern Kentucky University
Dan Curtin, Northern Kentucky University, host
Dick Davitt, University of Louisville
Richard Davitt, Universty of Louisville
Chuck Holmes, Miami University
David Kullman, Miami University
Danny Otero, Xavier University
Steve Pelikan, University of Cincinnati
Dick Pulskamp, Xavier University
Peter Yff, Ball State University
We met for dinner Friday evening at Buca di Beppo in Rookwood Commons.
This
restaurant is a shrine of Italian-American kitsch, but they offer
a wonderful
meal. We were sorry that Peter Yff had bad weather on the
way down from Chicago
that prevented him from meeting us at the restaurant; he joined
us at Xavier
afterwards.
We convened to read the paper "On an unsettled question in the theory
of
discontinuous groups," Quart. J. of Pure and Applied Math. 33 (1902)
230-238.
The discussion began with biographical information about Burnside,
extracted
primarily from Forsyth's obituary in J. London Math. Soc. 3, ii
(April 1928)
64-80, and Chapter 3 of Charles Curtis' "Frobenius, Burnside, Schur
and Brauer:
Pioneers of Representation Theory" (AMS, 1999).
On hand were copies of Burnside's Theory of Groups of Finite Order
(the Dover
reprint of the second edition of 1911); Carmichael's "Introduction
to the Theory
of Finite Groups" (the Dover 1956 reprint of the 1937 original);
and Narain
Gupta's survey article "On groups in which every element has finite
order" (Amer.
Math. Monthly 96, no. 4 (Apr 1989) 297-308), which provided a good
deal of
information about progress in the investigation of the Burnside
problem.
We made our way, with some difficulty in spots, through the first
four pages
of the paper on Friday evening, paying close attention to the use
of terminology ("self-conjugate" for "normal", "permutable" for "commuting").
The term
"independent operations" was the source of much discussion, since
it was
unclear what Burnside really meant by this. Christensen,
and especially
Holmes, provided guidance at crucial junctures in our attempts
to understand
what was going on.
An interesting discussion about the history of group theory in the
20th century,
with special attention to the importance of standard textbooks,
was a highlight
of the Saturday morning session. We completed the paper just
in time to adjourn
a few minutes after noon.
There was interest in accepting an invitation tendered by Della
Fenster, an
expert on the work of L. E. Dickson, to meet in Louisville to read
a paper
of Dickson's. This will be followed up in the coming weeks.
Respectfully submitted,
Danny Otero