1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Group theory

  1. Mar 26, 2005 #1
    i've just started out with a course in group theory...here's a question that's been bothering me for a while now...
    let G be a group and 'a' ,a unique element of order 2 in G. show that a belongs to Z(G).
    if every element of the group has order 2 this is pretty easy....but that's not the case. one thing i've noted is a = a^-1..but does that help?
  2. jcsd
  3. Mar 26, 2005 #2
    Given any x in G, what can be said about xax^-1? For example, what is its order?
  4. Mar 26, 2005 #3
    another question...

    well...thanks...the order of xax^-1 is 2....and a is the only element with order 2...so xax^-1=a and that implies the result.
    another problem that i seem to be unable to figure out is...
    f:(Zm , +m) --> (Zn,+n) is a group homomorphism where Zm and Zn denote groups of residue classes modulo m and n respectively. if m and n are relatively prime, then show that f is identically 0.
    i fathom we are supposed to use the relation.... (m,n)=1 implies am+bn =1 for some a and b in Z...how do you proceed further?
    thanks for the help...
  5. Mar 26, 2005 #4

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Lemma: if f is a group homomorphism from G to H then the order of f(g) divides the order of g

    Prove it and deduce the answer you want.

    the am+bn=1 won't help since you aren't actually doing anything with m and n together.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Group theory
  1. Group Theory (Replies: 10)

  2. Group theory (Replies: 3)

  3. Group Theory (Replies: 6)

  4. Group theory (Replies: 1)