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Math Help - group terminology

  1. #1
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    group terminology

    what is the group Z6 and the group Z3 x Z2. the numbers are subscripts btw
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  2. #2
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    Quote Originally Posted by poirot View Post
    what is the group Z6 and the group Z3 x Z2. the numbers are subscripts btw

    Both are one and the same: the cyclic group of order 6 .

    Tonio
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  3. #3
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    Quote Originally Posted by tonio View Post
    Both are one and the same: the cyclic group of order 6 .

    Tonio
    are they integers under addition, for example or is it just any cyclic group order 6? Thats what i'm after.
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    Quote Originally Posted by poirot View Post
    are they integers under addition, for example or is it just any cyclic group order 6? Thats what i'm after.

    \mathbb{Z}_n is a group under addition modulo n, and \mathbb{Z}_2\times \mathb{Z}_3 is a group under

    coordinatewise addition. Anyway, they both are isomorphic to a (or the, if you will) cyclic group of order 6.

    Tonio
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