1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Sylow theorems

  1. Jan 11, 2009 #1
    1. The problem statement, all variables and given/known data

    Let G be a group of order pem. Prove that G contains a subgroup of order pr for every integer r [tex]\leq[/tex]e

    3. The attempt at a solution

    By sylow 1 we know that there exists a subgroup of order pe. so that case is done, we need to show that supgroups of order r<e exist now.

    Thats tricky. im guessing this is an application of the the thrid sylow theorem but i dont know how to use it.

    s is the number of sylow p=subgroups. then s|m and is congruent to 1 mod p.

    so we know that s has to be at least e. dunno where to go from here.
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted