torsionfree simple linear groupby kimkibun Tags: abstract algebra, group theory, linear groups, research 

#1
Jul512, 12:06 PM

P: 30

im having my undergrad math thesis right now, and the topic that i want to choose is the existence of torsionfree simple linear groups. (which i found here: http:///www.sci.ccny.cuny.edu/~shpil...s/probmat.html)
i just want to know if this topic is recommended for undergrad? 



#2
Jul512, 10:12 PM

P: 606

The link is broken\doesn't exist. Check it, please About the subject: it sounds interesting but difficult. Right now I can't think of one single example that fulfills all the conditions, so I guess any such must be a rather vicious one. Anyway, the books by Wehrfritz, Humphreys, ShafarevichKostrikin or Springer are important to check. In particular, and since you may also want to consider topological groups and not merely abstract, discrete ones, Humphreys makes a nice observation: an almost simple algebraic group G (i.e., without closed connected normal subgroups except the trivial ones) is such that G/Z(G) is ALWAYS simple in the usual, abstract sense. DonAntonio 



#3
Jul712, 10:21 AM

P: 30

http://www.sci.ccny.cuny.edu/~shpil/...s/probmat.html i agree with you sir when it comes to difficulty. my professor said that its a suicide for a graduating student to choose such topic. well anyway, thank you sir for your reply. btw, i enjoy reading the book of ShafarevichKostrikin. 


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