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!

Conjugacy Class Problem

  1. Dec 1, 2008 #1
    1. The problem statement, all variables and given/known data
    If a group has order 20 has 4 conjugacy classes, it must have a trivial centre. True or False?


    2. Relevant equations
    The Class Equation

    3. The attempt at a solution
    I believed the answer to be false with this following counterexample:
    20 = lZ(G)l + (20/4 + 20/4 + 20/5 + 20/5) => order of Z(G) = 2 => the centre is non-trivial.
    where 5, 5, 4, 4 is the size of the 4 conjugate classes respectively

    Any feedback on my reasoning and any flaws are very much appreciated
     
  2. jcsd
  3. Dec 2, 2008 #2

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    You haven't demonstrated that such a group exists.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Conjugacy Class Problem
  1. Conjugacy Classes (Replies: 1)

  2. Conjugacy class (Replies: 1)

  3. Conjugacy classes (Replies: 0)

Loading...