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Math Help - group

  1. #1
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    group

    Let G be a group with |G|=30 .Prove that G is izomorf with the group of 30-th roots of unity .
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  2. #2
    Super Member Gamma's Avatar
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    Dec 2008
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    Iowa City, IA
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    Not true

    If a group has order 30 there are 4 unique groups (up to isomorphism) to which it could be isomorphic.
    Abelian
    1) \mathbb{Z}_{30} this is the one you are looking for
    Nonabelian
    2) D_{15} (Dihedral group)
    3) D_5 \times Z_3
    4) D_3 \times Z_5

    If its abelian its easy to see why it must be cyclic by the fundamental theorem of finitely generated abelian groups, and noting 30=2*3*5

    hope this helps
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