torsion-free simple linear group

kimkibun

im having my undergrad math thesis right now, and the topic that i want to choose is the existence of torsion-free 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?

DonAntonio

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, Shafarevich-Kostrikin 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

kimkibun

here's the link sir

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 Shafarevich-Kostrikin.