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Torsion-free simple linear group

  1. Jul 5, 2012 #1
    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/gworld/problems/probmat.html)

    i just want to know if this topic is recommended for undergrad?
  2. jcsd
  3. Jul 5, 2012 #2

    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.

  4. Jul 7, 2012 #3
    here's the link sir


    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.
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