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

Classification of groups

  1. Jan 10, 2008 #1
    I was wondering about the classification of groups with a certain number of subgroups. I (sort of mostly I think maybe) get the ideas behind classification of groups of a certain (hopefully small) order, but I came across a question about classifying all groups with exactly 4 subgroups, and I have no clue whatsoever how to even begin.
     
  2. jcsd
  3. Jan 11, 2008 #2

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    Well, any (nontrivial) group has at least two subgroups: itself and the subgroup consisting of only the identity. Moreover, a subgroup of a subgroup is a subgroup of the original group. Another thing you might find helpful is Cauchy's theorem.
     
  4. Jan 12, 2008 #3

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    sylow's theorem says there is a subgroup of order p^k whenever p is prime and p^k divides the order of the group. so groups of order pq seem to satisfy the condition. where p and q are prime. but there canniot be more than two factors of the order of the group, and there cannot be a factor occurring to a power higher than 2? or could a group of order p^3 possibly work? seems unlikely........
     
  5. Jan 12, 2008 #4
    Yeah, I think groups of order pq work. Also, I think a cyclic group of order p^3 works...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Classification of groups
  1. An Group (Replies: 1)

Loading...