Answer by Richard Lyons for Groups that do not exist
I believe that at some point there was a conjecture (by whom, I don't recall) that Janko's smallest group, of order $175,560=11(11^2-1)(11^3-1)/(11-1)$, should be the first of an infinite sequence of...
View ArticleAnswer by DavidLHarden for Groups that do not exist
There was a point during the history of the Classification when pursuers of sporadic groups distinguished the Baby Monster, the Middle Monster and the Super Monster. The first two actually turned out...
View ArticleAnswer by Geoff Robinson for Groups that do not exist
I tried to write a longer answer which froze, so I'll write a shorter version. You might look at the history of the "Solomon fusion system" which arose in a characterization problem undertaken by Ron...
View ArticleAnswer by Nick Gill for Groups that do not exist
I'm not sure if this is quite what you're looking for but....In this book "Finite simple groups", Gorenstein tells the story of Feit & Thompson's proof of the odd order theorem. Very roughly, it...
View ArticleGroups that do not exist
In the long process that resulted in the classification of finite simple groups, some of the exceptional groups were only shown to exist after people had computed (most of) their character tables and...
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