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Did any of you guys ever read those lines by Roland Schmidt where he talked about the terseness of articles in Group Theory in the days prior to the conclusion of the classification of the finite simple groups?

The complete story might have appeared in the Notices of the AMS, a similar publication, or an online recollection of group-theoretical anecdotes, but I'm not sure about it. All I can recall is that, at some point of his write-up, R. Schmidt brought up that famed Group Theory Year in UC (1960-1961) and a hilarious exploit by J. H. Conway and David Wales from the epoch.

I really hope that somebody out there has read it recently and can tell me where I can find it again.

Thanks.

Added (Nov 8/2010) The said Conway incident went something like this: "one day he (Professor Freese, as you can read in the first reply to the thread) found Conway and Wales working with some relations and generators. Conway and Wales said they wanted to see if it was a group what they had there. Professor Freese could not help but ask

How could it not be?,

to which, they immediately replied

It could be infinite!"

Added (Nov 19/2010) I'm sure that in that elusive note one could also find the following story:

"A typical journal page(?) in those days would look something like this

Theorem. All groups are finite.

Proof. Deny."

I also remember that I didn't really get the joke at the time, but that's another story...

Does anybody here remember reading something like this some time ago? C'mon fellas! I know I could not have been the only one in here to catch it back in the day.

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Are you perhaps thinking of the article "A Brief History of the Classification of the Finite Simple Groups" by Ronald Solomon, which appeared in the Bulletin in 2001? –  Faisal Nov 6 '10 at 1:18
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It doesn't sound right for J.H. Conway to be involved in the 1960-1961 group theory year in Chicago. I don't think he became interested in group theory until the mid-1960s. –  John Stillwell Nov 6 '10 at 3:30
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I'll go with the second option. –  J. H. S. Nov 21 '10 at 4:32
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I suggest you go with the first. –  S. Carnahan Nov 28 '10 at 6:10
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Aparently the interlocutor in this story was my adviser, Ralph Freese, who was a grad student at Caltech at the time. (I asked him about it over lunch today and he told me person (A) was David Wales.) I suggested he join MO and tell the story himself. Hopefully he will be here soon... –  William DeMeo Dec 10 '10 at 23:14

1 Answer 1

As William DeMeo says, I was the one who told this story. I was a grad student at CalTech from 1968-72. One quarter John Conway was visiting and working with David Wales, searching for finite simple groups. CalTech had an afternoon tea everyday. Conway and Wales had a group presentation on the blackboard and I asked what the problem was. They said they were trying to determine if it was a group. After a minute I got up the nerve to ask them how could it not be a group. They both turned to me and in unison said "It could be infinite!"

I believe this search did construct a simple group of order 145926144000 that Rudvalis had suggested might exist. It is sometimes called the Rudvalis-Conway-Wales group.

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Many thanks. This is great! I note for the record that it doesn't actually answer the original question, which was, where did JHS first read about the incident? –  Gerry Myerson Dec 11 '10 at 3:07
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Welcome to MathOverflow, Prof. Freese. Please feel free to contribute any Lattice Theory or Universal Algebra you may have brought with you. Or any other mathematics. I also recommend tea.mathoverflow.net to get a feel of how things work around here. Gerhard "Ask Me About System Design" Paseman, 2010.12.11 –  Gerhard Paseman Dec 11 '10 at 8:14

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