Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Sylow's Theorems question

  1. Jun 15, 2005 #1
    Why must a group of order 98 contain a subgroup of order 7?
    I would think that Sylow's 1st theorem implies there exists at least one Sylow-7-subgroup of order 49 and at least one Sylow-2-subgroup of order 2 (since 98=2x7x7).

    Ray Veldkamp
  2. jcsd
  3. Jun 15, 2005 #2
    7 is prime, 7 divides 98, hence by Cauchy's theorem there is an element of order 7. The subgroup generated by this element is of order 7.
  4. Jun 15, 2005 #3


    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    or because the stronger version of sylows theorems say there is always a subgroup of any prime power order that divides the order of the group, not just the maximal prime power order.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Sylow's Theorems question
  1. Sylow Question (Replies: 2)

  2. Sylow theorem part 2 (Replies: 1)