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Timeline for Group PGL(2,p) where p is prime

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Dec 20, 2012 at 10:25 comment added Nick Gill Jim, good comment. This is potentially a useful community-wiki type question for MO. Something like "What is the current status and priority of group-recognition questions?" Experts may then be able to explain (a) why a particular group-recognition question is useful, and (b) how much is known on the given question...
Dec 19, 2012 at 20:33 comment added Jim Humphreys Though "sara" has long since disappeared, your answer sheds better light on this kind of old problem, which is easy to formulate after a basic course in group theory. It's not so easy to resolve, but of course there is a long paper trail by now, including numerous multi-author papers (including the ones you cite) on the recognition problem relative to prime graphs or sets of element orders. Probably a more useful question than the one asked here would be whether any single source gives a complete survey of what's known and unknown at this point along with basic methods.
Dec 19, 2012 at 16:23 history answered Nick Gill CC BY-SA 3.0