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A while back I was learning about finite groups in an algebra class. I mentioned to a friend that finite group theory might be an interesting area of research to pursue. She asked something along the lines of "Isn't finite group theory 'done?' I thought that ended with the classification theorems."

I'm not sure how to answer. Is finite group theory still an active area of research? If so, what are some of the common problems that professors and graduate students are working on right now? Are there any reading materials to get more acquainted with such things?

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    I did some research on prime graphs of finite groups lately. I wouldn't say finite group theory is as active as before the classification theorems but there's still some smaller stuff going on. A lot of it is tied up with representation theory, for example monomial groups are still actively studied.2012-10-16
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    If you are interested, how a much improved proof of the classification of finite simple groups could look like, take a look at http://www.math.msu.edu/~meier/Preprints/CGP/cgp_abstract.html [This is a still active area, but technically quite difficult.]2012-10-16
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    http://www.ams.org/mathscinet/search/publications.html?pg6=CC&s6=20D&Submit=Search&dr=pubyear&yrop=gt&arg3=20092012-10-17
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    @JackSchmidt I guess your comment means that it is still a fruitful area of research (because there are so many publications later than 2009), but your link seems to require a subscription.2012-10-17
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    What about the (modular) characters of the FSG? Or the McKay conjecture? Or the cohomology of p-groups? Or minimal presentations of groups? Or... There are a fantastic amount of open questions, unexplored areas, and active research projects. Plus there are areas that "spring" from FGT, like fusion systems, subgroup complexes, cohomology varieties, etc. Certainly very very fruitful.2012-10-17
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    Thanks @SteveD, what does FSG stand for?2012-10-17
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    @NoomiHolloway FSG = finite simple groups.2012-10-18

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