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!

Groups of order 51 and 39 (Sylow theorems).

  1. Dec 9, 2009 #1
    1. The problem statement, all variables and given/known data

    a) Classify all groups of order 51.
    b) Classify all groups of order 39.

    2. Relevant equations
    Sylow theorems.
    3. The attempt at a solution

    a) C51
    b) Z3 X Z13
    and Z13 x Z3, the semi-direct product with presentation <a,b|a13=b3=1, ab=a3 >


    Are these all of the groups? Am I missing any? Do you think these are sufficient answers?
    Thank you!
     
  2. jcsd
  3. Dec 9, 2009 #2

    Mark44

    Staff: Mentor

    51 is not prime...
     
  4. Dec 13, 2009 #3
    Yes, I understand that 51 is not a prime, but 51 is a multiple of 3 and 17.

    So, I'm using this theorem:

    Theorem 1. Suppose G is a non-Abelian group whose order is divisible by at least two
    distinct primes and all of whose proper subgroups have prime-power order. Then
    (i) absolutevalue[G] = p" q where p and q are primes;
    (ii) the Sylow p-subgroup of G is the unique nontrivial proper normal subgroup of G and
    is elementary Abelian;
    (iii) absolutevalue[G'] = p";
    (iv) absolutevalue[Z(G)] = 1;
    (v) G has p" Sylow q-subgroups and when n > 1, q divides (p" - t)/(p - 1).

    I know that groups of order 3 are the C3.
    Groups of order 17 are C17.
    So, I think that 51 must be C51.
    Any help would be appreciated!
     
    Last edited: Dec 13, 2009
  5. Dec 16, 2009 #4
    i'm telling tyler
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Groups of order 51 and 39 (Sylow theorems).
Loading...