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Group theory convention

  1. Oct 23, 2011 #1
    1. The problem statement, all variables and given/known data
    I've just started to study group theory, and i keep encountering questions where no operators are specified so i was wondering if there was a conventional operator that was meant to be used. For instance I had a question to prove that a cyclic group of order 14 is isomorphic with Z mod 14. This is true under addition but not under multiplication so should i presume that Z14 with unspecified operator is addition?


    2. Relevant equations
    None.


    3. The attempt at a solution
     
  2. jcsd
  3. Oct 23, 2011 #2

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    Welcome to PF, chinye11! :smile:

    Z/14Z is not a group under multiplication.
    (Why not?)

    So it has to be addition.
    As a bonus it is isomorphic to C14 (also written as Z14).
     
  4. Oct 23, 2011 #3
    Z/14 is not a group under multiplication because not every element has an inverse, my bad didn't check it.
     
  5. Oct 23, 2011 #4

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    Yep!

    The group Z mod 14 with multiplication is denoted as (Z/14Z)x or as (Z/14Z)*.
    That is, the same set, but with all elements that do not have an inverse removed.
     
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